Download - Geometry AMS
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Bridging Geometry Concepts with Art
by Joan A. Cotter, [email protected]
AMS ConferenceMarch 17, 2012
San Francisco CA
Presentations available: rightstartmath.com
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2 © Joan A. Cotter, 2012
Drawing ToolsPaper
North American paper11 in. by 8.5 in.
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3 © Joan A. Cotter, 2012
Drawing ToolsPaper
International paper21.0cm by 29.7cm
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4 © Joan A. Cotter, 2012
Drawing ToolsDrawing board with paper
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5 © Joan A. Cotter, 2012
Drawing ToolsDrawing board with paper
Affix tape only at the top.
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6 © Joan A. Cotter, 2012
Drawing ToolsT-square
T-square
Right-handed user.
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7 © Joan A. Cotter, 2012
Drawing ToolsT-square
Left-handed user.
T-square
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8 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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9 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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10 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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11 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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12 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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13 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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14 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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15 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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16 © Joan A. Cotter, 2012
Drawing ToolsT-square
Must hug the edge of the board.
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17 © Joan A. Cotter, 2012
Drawing ToolsPencil (mechanical) and eraser
Hold pencil 2-3cm (1 in.) from tip.
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18 © Joan A. Cotter, 2012
Drawing ToolsPencil (mechanical) and eraser
Hold pencil 2-3cm (1 in.) from tip.
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19 © Joan A. Cotter, 2012
Drawing ToolsPencil (mechanical) and eraser
Hold pencil 2-3cm (1 in.) from tip.
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20 © Joan A. Cotter, 2012
Drawing ToolsPencil (mechanical) and eraser
An eraser is an essential tool.
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21 © Joan A. Cotter, 2012
Drawing ToolsPencil (mechanical) and eraser
Parallel lines.
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22 © Joan A. Cotter, 2012
Drawing ToolsPencil (mechanical) and eraser
Parallel lines.
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23 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle (a set square)
60°
30°
90°
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24 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
Triangle must hug the t-square.
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25 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
This doesn’t work!
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26 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
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27 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
More parallel lines.
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28 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
More parallel lines.
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29 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
Perpendicular lines.
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30 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
Perpendicular lines.
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31 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
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32 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
Still more parallel lines.
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33 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
Still more parallel lines.
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34 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
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35 © Joan A. Cotter, 2012
Drawing ToolsThe 30-60 triangle
Intersecting lines.
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36 © Joan A. Cotter, 2012
Drawing ToolsThe 45 triangle
45°
45° 90°
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37 © Joan A. Cotter, 2012
Drawing ToolsThe 45 triangle
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38 © Joan A. Cotter, 2012
Drawing ToolsThe 45 triangle
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39 © Joan A. Cotter, 2012
Drawing ToolsThe 45 triangle
Maintain a margin.
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40 © Joan A. Cotter, 2012
Drawing ToolsThe 45 triangle
Maintain a margin.
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41 © Joan A. Cotter, 2012
Drawing ToolsThe 45 triangle
Maintain a margin.
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42 © Joan A. Cotter, 2012
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43 © Joan A. Cotter, 2012
Equilateral TrianglesDraw the base line
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44 © Joan A. Cotter, 2012
Equilateral TrianglesDraw the base line
Move the t-square down.
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45 © Joan A. Cotter, 2012
Equilateral Triangles
Move the t-square down.
Draw the base line
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46 © Joan A. Cotter, 2012
Equilateral Triangles
Draw a side.
Draw the sides
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47 © Joan A. Cotter, 2012
Equilateral Triangles
Flip the triangle and repeat.
Draw the sides
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48 © Joan A. Cotter, 2012
Equilateral Triangles
Flip the triangle and repeat.
Draw the sides
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49 © Joan A. Cotter, 2012
Equilateral Triangles
A bit of erasing.
Draw the sides
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50 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
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51 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
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52 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
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53 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
12
12
The two halves are congruent.
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54 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
Divide it in half another way.
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55 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
Divide it in half another way.
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56 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
Divide it in half another way.
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57 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
Divide it in half another way.
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58 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into halves
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59 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into thirds
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60 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into thirds
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61 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into thirds
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62 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into thirds
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63 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into thirds
A bit of erasing.
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64 © Joan A. Cotter, 2012
Equilateral Triangles
Flip the triangle and repeat.
Divide it into thirds
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65 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into thirds
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66 © Joan A. Cotter, 2012
Equilateral Triangles
13
13
13
Divide it into thirds
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67 © Joan A. Cotter, 2012
Equilateral Triangles
13
13
13
Can you figure out how to do it?
Divide it into thirds
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68 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
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69 © Joan A. Cotter, 2012
Equilateral Triangles
Finding the center of the base line.
Divide it into fourths
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70 © Joan A. Cotter, 2012
Equilateral Triangles
Be sure the tick mark intersects the line.
tick mark
Divide it into fourths
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71 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
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72 © Joan A. Cotter, 2012
Equilateral Triangles
Flip the triangle over and repeat.
Divide it into fourths
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73 © Joan A. Cotter, 2012
Equilateral Triangles
How do you draw the last line?
Divide it into fourths
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74 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
How do you draw the last line?
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75 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
The smaller triangles are similar to the larger triangle.
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76 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
14
14
14
14
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77 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses:
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78 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses: ABDF,
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79 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses. ABDF, BCDF,
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80 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses: ABDF, BCDF, BDEF.
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81 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids:
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82 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids: BCEF,
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83 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids: BCEF, ACDF,
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84 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids: BCEF, ACDF, ABDE.
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85 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
Cut it out….
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86 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
and fold on the lines.
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87 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
and fold on the lines.
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88 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
and fold on the dotted lines.
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89 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
and fold on the dotted lines.
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90 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
and fold on the dotted lines.
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91 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
and fold on the dotted lines.
![Page 92: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/92.jpg)
92 © Joan A. Cotter, 2012
Equilateral TrianglesTetrahedron
and fold on the dotted lines.
![Page 93: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/93.jpg)
93 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into eighths
How could you draw eighths?
![Page 94: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/94.jpg)
94 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into eighths
![Page 95: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/95.jpg)
95 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into eighths
![Page 96: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/96.jpg)
96 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into eighths
Not very esthetic.
![Page 97: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/97.jpg)
97 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into eighths
![Page 98: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/98.jpg)
98 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Can you divide it into sixths?
![Page 99: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/99.jpg)
99 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Can you divide it into sixths?
![Page 100: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/100.jpg)
100 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
![Page 101: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/101.jpg)
101 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
![Page 102: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/102.jpg)
102 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name an acute triangle:
A
B
CD
E
FG
![Page 103: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/103.jpg)
103 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name an acute triangle: ACE.
A
B
CD
E
FG
![Page 104: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/104.jpg)
104 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name a right triangle:
A
B
CD
E
FG
![Page 105: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/105.jpg)
105 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name a right triangle: ADE,
A
B
CD
E
FG
![Page 106: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/106.jpg)
106 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name a right triangle: ADE, ABE,
A
B
CD
E
FG
![Page 107: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/107.jpg)
107 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name a right triangle: ADE, ABE, ABG.
A
B
CD
E
FG
![Page 108: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/108.jpg)
108 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name an obtuse triangle:
A
B
CD
E
FG
![Page 109: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/109.jpg)
109 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into sixths
Name an obtuse triangle: GCE.
A
B
CD
E
FG
![Page 110: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/110.jpg)
110 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
Can you divide it into twelfths?
![Page 111: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/111.jpg)
111 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
![Page 112: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/112.jpg)
112 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
![Page 113: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/113.jpg)
113 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
![Page 114: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/114.jpg)
114 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
![Page 115: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/115.jpg)
115 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
![Page 116: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/116.jpg)
116 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
Do you see the cube?
![Page 117: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/117.jpg)
117 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
Do you see the cube?
![Page 118: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/118.jpg)
118 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
Do you see the hexagon?
![Page 119: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/119.jpg)
119 © Joan A. Cotter, 2012
Equilateral TrianglesDivide it into twelfths
Do you see the hexagon?
![Page 120: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/120.jpg)
120 © Joan A. Cotter, 2012
Equilateral Triangles
Ninths
![Page 121: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/121.jpg)
121 © Joan A. Cotter, 2012
Equilateral Triangles
Twenty-sevenths
![Page 122: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/122.jpg)
122 © Joan A. Cotter, 2012
Equilateral Triangles
Twenty-sevenths
![Page 123: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/123.jpg)
123 © Joan A. Cotter, 2012
Equilateral Triangles
Twenty-sevenths
![Page 124: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/124.jpg)
124 © Joan A. Cotter, 2012
Equilateral Triangles
Twenty-sevenths
![Page 125: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/125.jpg)
125 © Joan A. Cotter, 2012
Equilateral Triangles
Thirty-seconds
![Page 126: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/126.jpg)
126 © Joan A. Cotter, 2012
Equilateral Triangles
Stephanie, 6, a Montessori child, did 256.
![Page 127: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/127.jpg)
127 © Joan A. Cotter, 2012
Equilateral Triangles
Stephanie, 6, a Montessori child, did 256.
![Page 128: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/128.jpg)
128 © Joan A. Cotter, 2012
Equilateral Triangles
Stephanie, 6, a Montessori child, did 256.
![Page 129: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/129.jpg)
129 © Joan A. Cotter, 2012
Equilateral Triangles
Stephanie, 6, a Montessori child, did 256.
![Page 130: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/130.jpg)
130 © Joan A. Cotter, 2012
Equilateral Triangles
Stephanie, 6, a Montessori child, did 256.
![Page 131: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/131.jpg)
131 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 132: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/132.jpg)
132 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 133: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/133.jpg)
133 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 134: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/134.jpg)
134 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 135: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/135.jpg)
135 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 136: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/136.jpg)
136 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 137: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/137.jpg)
137 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 138: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/138.jpg)
138 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 139: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/139.jpg)
139 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 140: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/140.jpg)
140 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
From Psychogeometry
![Page 141: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/141.jpg)
141 © Joan A. Cotter, 2012
Equilateral TrianglesSpiral
![Page 142: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/142.jpg)
142 © Joan A. Cotter, 2012
![Page 143: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/143.jpg)
143 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
![Page 144: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/144.jpg)
144 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
![Page 145: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/145.jpg)
145 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
![Page 146: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/146.jpg)
146 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
![Page 147: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/147.jpg)
147 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
![Page 148: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/148.jpg)
148 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
![Page 149: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/149.jpg)
149 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
A bit of erasing.
![Page 150: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/150.jpg)
150 © Joan A. Cotter, 2012
HexagonsStart with an equilateral triangle
![Page 151: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/151.jpg)
151 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 152: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/152.jpg)
152 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 153: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/153.jpg)
153 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 154: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/154.jpg)
154 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
Flip the triangle and repeat.
![Page 155: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/155.jpg)
155 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 156: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/156.jpg)
156 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 157: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/157.jpg)
157 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 158: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/158.jpg)
158 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 159: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/159.jpg)
159 © Joan A. Cotter, 2012
HexagonsStart with a small equilateral triangle
![Page 160: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/160.jpg)
160 © Joan A. Cotter, 2012
HexagonsDraw all the diagonals
![Page 161: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/161.jpg)
161 © Joan A. Cotter, 2012
HexagonsDraw all the diagonals
![Page 162: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/162.jpg)
162 © Joan A. Cotter, 2012
HexagonsDraw all the diagonals
![Page 163: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/163.jpg)
163 © Joan A. Cotter, 2012
HexagonsDraw all the diagonals
![Page 164: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/164.jpg)
164 © Joan A. Cotter, 2012
HexagonsDraw all the diagonals
![Page 165: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/165.jpg)
165 © Joan A. Cotter, 2012
HexagonsDraw all the diagonals
![Page 166: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/166.jpg)
166 © Joan A. Cotter, 2012
HexagonsFind the figures
Another hexagon.
![Page 167: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/167.jpg)
167 © Joan A. Cotter, 2012
HexagonsFind the figures
Another hexagon.
![Page 168: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/168.jpg)
168 © Joan A. Cotter, 2012
HexagonsFind the figures
2 non-congruent rectangles.
![Page 169: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/169.jpg)
169 © Joan A. Cotter, 2012
HexagonsFind the figures
2 non-congruent rectangles.
![Page 170: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/170.jpg)
170 © Joan A. Cotter, 2012
HexagonsFind the figures
2 non-congruent rectangles.
![Page 171: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/171.jpg)
171 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent right triangles.
![Page 172: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/172.jpg)
172 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent right triangles.
![Page 173: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/173.jpg)
173 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent right triangles.
![Page 174: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/174.jpg)
174 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent right triangles.
![Page 175: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/175.jpg)
175 © Joan A. Cotter, 2012
HexagonsFind the figures
2 non-congruent rhombuses.
![Page 176: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/176.jpg)
176 © Joan A. Cotter, 2012
HexagonsFind the figures
2 non-congruent rhombuses.
![Page 177: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/177.jpg)
177 © Joan A. Cotter, 2012
HexagonsFind the figures
2 non-congruent rhombuses.
![Page 178: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/178.jpg)
178 © Joan A. Cotter, 2012
HexagonsFind the figures
3 similar equilateral triangles.
![Page 179: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/179.jpg)
179 © Joan A. Cotter, 2012
HexagonsFind the figures
3 similar equilateral triangles.
![Page 180: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/180.jpg)
180 © Joan A. Cotter, 2012
HexagonsFind the figures
3 similar equilateral triangles.
![Page 181: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/181.jpg)
181 © Joan A. Cotter, 2012
HexagonsFind the figures
3 similar obtuse triangles.
![Page 182: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/182.jpg)
182 © Joan A. Cotter, 2012
HexagonsFind the figures
3 similar obtuse triangles.
![Page 183: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/183.jpg)
183 © Joan A. Cotter, 2012
HexagonsFind the figures
3 similar obtuse triangles.
![Page 184: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/184.jpg)
184 © Joan A. Cotter, 2012
HexagonsFind the figures
3 similar obtuse triangles.
![Page 185: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/185.jpg)
185 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent trapezoids.
![Page 186: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/186.jpg)
186 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent trapezoids.
![Page 187: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/187.jpg)
187 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent trapezoids.
![Page 188: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/188.jpg)
188 © Joan A. Cotter, 2012
HexagonsFind the figures
3 non-congruent trapezoids.
![Page 189: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/189.jpg)
189 © Joan A. Cotter, 2012
HexagonsFind the figures
2 similar kites.
![Page 190: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/190.jpg)
190 © Joan A. Cotter, 2012
HexagonsFind the figures
2 similar kites.
![Page 191: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/191.jpg)
191 © Joan A. Cotter, 2012
HexagonsFind the figures
2 similar kites.
![Page 192: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/192.jpg)
192 © Joan A. Cotter, 2012
HexagonsConstruct the small star
Apothem: perpendicular line from side to center.
![Page 193: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/193.jpg)
193 © Joan A. Cotter, 2012
HexagonsConstruct the small star
Apothem: perpendicular line from side to center.
![Page 194: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/194.jpg)
194 © Joan A. Cotter, 2012
HexagonsConstruct the small star
Apothem: perpendicular line from side to center.
![Page 195: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/195.jpg)
195 © Joan A. Cotter, 2012
HexagonsConstruct the small star
![Page 196: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/196.jpg)
196 © Joan A. Cotter, 2012
HexagonsConstruct the small star
![Page 197: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/197.jpg)
197 © Joan A. Cotter, 2012
HexagonsConstruct the small star
![Page 198: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/198.jpg)
198 © Joan A. Cotter, 2012
HexagonsConstruct the small star
![Page 199: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/199.jpg)
199 © Joan A. Cotter, 2012
HexagonsConstruct the small star
Ratio of the areas of star and hexagon?
![Page 200: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/200.jpg)
200 © Joan A. Cotter, 2012
HexagonsConstruct the small star
Ratio of the areas of star and hexagon?
![Page 201: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/201.jpg)
201 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 202: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/202.jpg)
202 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 203: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/203.jpg)
203 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 204: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/204.jpg)
204 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 205: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/205.jpg)
205 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 206: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/206.jpg)
206 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 207: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/207.jpg)
207 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 208: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/208.jpg)
208 © Joan A. Cotter, 2012
HexagonsConstruct the large star
![Page 209: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/209.jpg)
209 © Joan A. Cotter, 2012
![Page 210: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/210.jpg)
210 © Joan A. Cotter, 2012
The Clock112
23
4567
8910
11
![Page 211: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/211.jpg)
211 © Joan A. Cotter, 2012
The Clock112
23
4567
8910
11
![Page 212: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/212.jpg)
212 © Joan A. Cotter, 2012
The Clock112
23
4567
8910
11
![Page 213: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/213.jpg)
213 © Joan A. Cotter, 2012
The Clock112
23
4567
8910
11
![Page 214: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/214.jpg)
214 © Joan A. Cotter, 2012
The Clock112
23
4567
8910
11
![Page 215: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/215.jpg)
215 © Joan A. Cotter, 2012
The Clock
12 12
3
4567
8
9
1011
11223
4567
8910
11
![Page 216: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/216.jpg)
216 © Joan A. Cotter, 2012
![Page 217: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/217.jpg)
217 © Joan A. Cotter, 2012
Squares
The 45 triangle.
![Page 218: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/218.jpg)
218 © Joan A. Cotter, 2012
Squares
The 45 triangle is half of a square.
![Page 219: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/219.jpg)
219 © Joan A. Cotter, 2012
SquaresConstruct a square
Draw the base line.
![Page 220: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/220.jpg)
220 © Joan A. Cotter, 2012
Squares
Move the t-square down.
Construct a square
![Page 221: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/221.jpg)
221 © Joan A. Cotter, 2012
Squares
Move the t-square down.
Construct a square
![Page 222: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/222.jpg)
222 © Joan A. Cotter, 2012
Squares
Draw the sides.
Construct a square
![Page 223: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/223.jpg)
223 © Joan A. Cotter, 2012
Squares
Draw the diagonal…
Construct a square
![Page 224: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/224.jpg)
224 © Joan A. Cotter, 2012
Squares
or just a tick mark.
Construct a square
![Page 225: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/225.jpg)
225 © Joan A. Cotter, 2012
Squares
Draw the top.
Construct a square
![Page 226: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/226.jpg)
226 © Joan A. Cotter, 2012
Squares
A bit of erasing.
Construct a square
![Page 227: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/227.jpg)
227 © Joan A. Cotter, 2012
SquaresConstruct a square
![Page 228: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/228.jpg)
228 © Joan A. Cotter, 2012
SquaresHalves
![Page 229: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/229.jpg)
229 © Joan A. Cotter, 2012
SquaresHalves
![Page 230: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/230.jpg)
230 © Joan A. Cotter, 2012
SquaresFourths
![Page 231: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/231.jpg)
231 © Joan A. Cotter, 2012
SquaresEighths
![Page 232: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/232.jpg)
232 © Joan A. Cotter, 2012
SquaresSixteenths
![Page 233: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/233.jpg)
233 © Joan A. Cotter, 2012
SquaresSixteenths
![Page 234: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/234.jpg)
234 © Joan A. Cotter, 2012
SquaresHalves
We need to find the center.
![Page 235: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/235.jpg)
235 © Joan A. Cotter, 2012
SquaresHalves
We need to find the center.
![Page 236: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/236.jpg)
236 © Joan A. Cotter, 2012
SquaresHalves
We need to find the center.
![Page 237: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/237.jpg)
237 © Joan A. Cotter, 2012
SquaresHalves
We need to find the center.
![Page 238: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/238.jpg)
238 © Joan A. Cotter, 2012
SquaresHalves
![Page 239: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/239.jpg)
239 © Joan A. Cotter, 2012
SquaresFourths
![Page 240: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/240.jpg)
240 © Joan A. Cotter, 2012
SquaresFourths
![Page 241: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/241.jpg)
241 © Joan A. Cotter, 2012
SquaresEighths
Find the center of a small square.
![Page 242: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/242.jpg)
242 © Joan A. Cotter, 2012
SquaresEighths
Find the center of a small square.
![Page 243: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/243.jpg)
243 © Joan A. Cotter, 2012
SquaresEighths
Find the center of a small square.
![Page 244: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/244.jpg)
244 © Joan A. Cotter, 2012
SquaresEighths
Find the center of a small square.
![Page 245: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/245.jpg)
245 © Joan A. Cotter, 2012
SquaresEighths
Repeat for the other line.
![Page 246: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/246.jpg)
246 © Joan A. Cotter, 2012
SquaresEighths
![Page 247: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/247.jpg)
247 © Joan A. Cotter, 2012
SquaresSixteenths
![Page 248: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/248.jpg)
248 © Joan A. Cotter, 2012
SquaresSixteenths
![Page 249: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/249.jpg)
249 © Joan A. Cotter, 2012
SquaresSixteenths
![Page 250: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/250.jpg)
250 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 251: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/251.jpg)
251 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 252: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/252.jpg)
252 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 253: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/253.jpg)
253 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 254: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/254.jpg)
254 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 255: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/255.jpg)
255 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 256: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/256.jpg)
256 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 257: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/257.jpg)
257 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 258: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/258.jpg)
258 © Joan A. Cotter, 2012
SquaresRight triangle spiral
![Page 259: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/259.jpg)
259 © Joan A. Cotter, 2012
SquaresRight triangle spiral
Adapted from Psychogeometry
![Page 260: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/260.jpg)
260 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 261: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/261.jpg)
261 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 262: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/262.jpg)
262 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 263: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/263.jpg)
263 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 264: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/264.jpg)
264 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 265: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/265.jpg)
265 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 266: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/266.jpg)
266 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 267: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/267.jpg)
267 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 268: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/268.jpg)
268 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 269: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/269.jpg)
269 © Joan A. Cotter, 2012
SquaresRight triangle design
![Page 270: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/270.jpg)
270 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 271: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/271.jpg)
271 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 272: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/272.jpg)
272 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 273: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/273.jpg)
273 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 274: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/274.jpg)
274 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 275: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/275.jpg)
275 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 276: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/276.jpg)
276 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 277: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/277.jpg)
277 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 278: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/278.jpg)
278 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 279: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/279.jpg)
279 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 280: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/280.jpg)
280 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 281: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/281.jpg)
281 © Joan A. Cotter, 2012
SquaresCircumscribed squares
![Page 282: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/282.jpg)
282 © Joan A. Cotter, 2012
SquaresInscribed squares
![Page 283: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/283.jpg)
283 © Joan A. Cotter, 2012
SquaresInscribed squares
![Page 284: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/284.jpg)
284 © Joan A. Cotter, 2012
SquaresInscribed squares
![Page 285: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/285.jpg)
285 © Joan A. Cotter, 2012
SquaresInscribed squares
Compare the area of the squares.
![Page 286: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/286.jpg)
286 © Joan A. Cotter, 2012
SquaresInscribed squares
Compare the area of the squares.
![Page 287: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/287.jpg)
287 © Joan A. Cotter, 2012
SquaresInscribed squares
![Page 288: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/288.jpg)
288 © Joan A. Cotter, 2012
SquaresInscribed squares
![Page 289: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/289.jpg)
289 © Joan A. Cotter, 2012
SquaresInscribed squares
![Page 290: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/290.jpg)
290 © Joan A. Cotter, 2012
SquaresInscribed squares
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291 © Joan A. Cotter, 2012
SquaresInscribed squares
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292 © Joan A. Cotter, 2012
SquaresInscribed squares
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293 © Joan A. Cotter, 2012
SquaresInscribed squares
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294 © Joan A. Cotter, 2012
SquaresInscribed squares
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295 © Joan A. Cotter, 2012
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296 © Joan A. Cotter, 2012
TangramsConstructing a tangram
![Page 297: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/297.jpg)
297 © Joan A. Cotter, 2012
TangramsConstructing a tangram
![Page 298: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/298.jpg)
298 © Joan A. Cotter, 2012
TangramsConstructing a tangram
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299 © Joan A. Cotter, 2012
TangramsConstructing a tangram
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300 © Joan A. Cotter, 2012
TangramsConstructing a tangram
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301 © Joan A. Cotter, 2012
TangramsConstructing a tangram
![Page 302: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/302.jpg)
302 © Joan A. Cotter, 2012
TangramsConstructing a tangram
![Page 303: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/303.jpg)
303 © Joan A. Cotter, 2012
TangramsConstructing a tangram
3 green figures are equal in area.
![Page 304: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/304.jpg)
304 © Joan A. Cotter, 2012
TangramsConstructing a tangram
3 green figures are equal in area.
![Page 305: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/305.jpg)
305 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 306: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/306.jpg)
306 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 307: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/307.jpg)
307 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 308: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/308.jpg)
308 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 309: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/309.jpg)
309 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 310: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/310.jpg)
310 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 311: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/311.jpg)
311 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 312: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/312.jpg)
312 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 313: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/313.jpg)
313 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
No tracing or measuring.
![Page 314: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/314.jpg)
314 © Joan A. Cotter, 2012
TangramsConstruct a tangram arrangement
More examples to construct.
![Page 315: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/315.jpg)
315 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Use the left side of the paper.
![Page 316: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/316.jpg)
316 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Start at the left side of the paper.
![Page 317: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/317.jpg)
317 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 318: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/318.jpg)
318 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 319: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/319.jpg)
319 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 320: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/320.jpg)
320 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 321: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/321.jpg)
321 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 322: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/322.jpg)
322 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 323: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/323.jpg)
323 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 324: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/324.jpg)
324 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 325: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/325.jpg)
325 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 326: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/326.jpg)
326 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 327: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/327.jpg)
327 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
Reflect the image across the line.
![Page 328: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/328.jpg)
328 © Joan A. Cotter, 2012
TangramsConstruct a tangram reflection
![Page 329: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/329.jpg)
329 © Joan A. Cotter, 2012
![Page 330: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/330.jpg)
330 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
First construct a right triangle.
![Page 331: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/331.jpg)
331 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 332: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/332.jpg)
332 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 333: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/333.jpg)
333 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 334: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/334.jpg)
334 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 335: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/335.jpg)
335 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 336: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/336.jpg)
336 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 337: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/337.jpg)
337 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 338: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/338.jpg)
338 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 339: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/339.jpg)
339 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Area of blue squares = yellow sq.
![Page 340: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/340.jpg)
340 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Area of blue squares = yellow sq.
![Page 341: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/341.jpg)
341 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Draw a right triangle.
![Page 342: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/342.jpg)
342 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 343: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/343.jpg)
343 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 344: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/344.jpg)
344 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 345: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/345.jpg)
345 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 346: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/346.jpg)
346 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 347: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/347.jpg)
347 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 348: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/348.jpg)
348 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Turn the t-square upside down.
![Page 349: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/349.jpg)
349 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 350: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/350.jpg)
350 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 351: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/351.jpg)
351 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 352: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/352.jpg)
352 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Do not move the t-square.
![Page 353: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/353.jpg)
353 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Do not move the t-square.
![Page 354: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/354.jpg)
354 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Do not move the t-square.
![Page 355: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/355.jpg)
355 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Do not move the t-square.
![Page 356: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/356.jpg)
356 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
![Page 357: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/357.jpg)
357 © Joan A. Cotter, 2012
Pythagorean TheoremConstruct squares on all sides
Area of blue squares = yellow sq.
![Page 358: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/358.jpg)
358 © Joan A. Cotter, 2012
![Page 359: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/359.jpg)
359 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
A
CB
![Page 360: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/360.jpg)
360 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
Draw the altitude.
A
CB
![Page 361: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/361.jpg)
361 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
Area is half of enclosing rectangle.
CB
A
![Page 362: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/362.jpg)
362 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
Another altitude. Find area.
CB
A
![Page 363: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/363.jpg)
363 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
Another altitude. Find area.
CB
A
![Page 364: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/364.jpg)
364 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
Another altitude. Find area.
A
CB
![Page 365: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/365.jpg)
365 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
Another altitude. Find area.
A
CB
![Page 366: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/366.jpg)
366 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
Altitudes intersect at the orthocenter.
A
CB
![Page 367: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/367.jpg)
367 © Joan A. Cotter, 2012
Triangle AreaConstruct the altitude
3 areas slightly different. Why?
A
CB
![Page 368: Geometry AMS](https://reader035.vdocument.in/reader035/viewer/2022081412/54568902af79590d0d8b4fce/html5/thumbnails/368.jpg)
Bridging Geometry Concepts with Art
by Joan A. Cotter, [email protected]
AMS ConferenceMarch 17, 2012
San Francisco CA
Presentations available: rightstartmath.com