g eometry p resentation #2 l ine and a ngle r elationships & c lassifying p olygons a pril 23,...
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GEOMETRY PRESENTATION #2LINE AND ANGLE RELATIONSHIPS & CLASSIFYING POLYGONSAPRIL 23, 2013MATH BLOCK 4Learning Objectives:
Identify parallel, perpendicular, and skew lines, and angles formed by a transversal
Identify and name polygons
Vocabulary
perpendicular linesparallel linesskew linesadjacent anglesvertical anglestransversal
When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines measure 90°, the lines are perpendicular lines.
Some lines in the same plane do not intersect at all. These lines are parallel lines. Segments and rays that are part of parallel lines are also parallel.
Skew lines do not intersect, and yet they are also not parallel. They lie in different planes.
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1: Identifying Parallel, Perpendicular, and Skew Lines
The lines appear to intersect to form right angles.
UV and YV
UV YV
XU and WZ
XU and WZ are skew.
The lines are in different planes and do not intersect.
XY and WZ
XY || WZ
The lines are in the same plane and do not intersect.
Tell whether the lines appear parallel, perpendicular, or skew.
Check It Out: Example 1A
The lines appear to intersect to form right angles.
WX and XUWX XU
Tell whether the lines appear parallel, perpendicular, or skew.
Check It Out: Example 1B
The lines are in different planes and do not intersect.
WX and UV
WX and UV are skew.
Tell whether the lines appear parallel, perpendicular, or skew.
Check It Out: Example 1C
The lines are in the same plane and do not intersect.
WX and ZY
WX || ZY
Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementaryVertical angles are the opposite angles formed by two intersecting lines. Angles 1 and 3 in the diagram are vertical angles. Vertical angles have the same measure, so they are congruent.
Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.
Reading Math
A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.
Line n line p. Find the measure of the angle.
Additional Example 2A: Using Angle Relationships to Find Angle Measures
22 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.
Line n line p. Find the measure of the angle.
Additional Example 2B: Using Angle Relationships to Find Angle Measures
3
m3 + 130° = 180°
–130° –130°
m3 = 50°
Adjacent angles formed by two intersecting lines are supplementary.
Subtract 130° to isolate m3.
Line n line p. Find the measure of the angle.
Additional Example 2C: Using Angle Relationships to Find Angle Measures
4
Alternate interior angles are congruent. m4 = 130°.
Lesson Homework – Bring Answers to next class
Tell whether the lines appear parallel, perpendicular, or skew.
1. AB and CD
2. EF and FH
3. AB and CG
4. In the figure on the right, line x || line y.
Identify the measures of 2, 6, and 7.
A. 70°, 110°, 70°
B. 110°, 70°, 70°
C. 70°, 70°, 110°
Triangles and rectangles are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. Each line segment forms a side of the polygon, and meets, but does not cross, another line segment at a common point. This common point is a vertex of a polygon.
The polygon atleft has sixsides and sixvertices.
Vertices is plural for vertex.
Remember!
Side
Vertex
Determine whether each figure is a polygon. If it is not, explain why not.
Additional Example 1: Identifying Polygons
A. B.
The figure is a polygon. It is a closed figure with 4 line segments.
The figure is not a polygon. It is not a closed figure.
Determine whether each figure is a polygon. If it is not, explain why not.
Additional Example 1: Identifying Polygons
C. D.
The figure is not a polygon. The figure is not formed by line segments.
The figure is not a polygon. There are line segments in the figure that intersect.
Polygons are classified by the number of sidesand angles they have.
Triangle3 sides
3 angles
Quadrilateral4 sides
4 angles
Pentagon5 sides
5 angles
Hexagon6 sides
6 angles
Heptagon7 sides
7 angles
Octagon8 sides
8 angles
Nonagon9 sides
9 angles
Decagon10 sides
10 angles
Name each polygon.
Additional Example 2: Classifying Polygons
A.
Octagon
B.
Quadrilateral
Check It Out: Example 2
Name each polygon.
A. B.
Quadrilateral Pentagon
A regular polygon is a polygon in which all sides are congruent and all angles are congruent.
Additional Example 3: Identifying and Classifying Regular Polygons
Name each polygon and tell whether it is aregular polygon. If it is not, explain why not.
The figure is a regularquadrilateral. A regular quadrilateral is also called a square.
The figure is aquadrilateral. It is an irregular polygon because all of the sides are not congruent.
A. B.
Lesson Homework – Bring Answers to next class
Determine whether each figure is a polygon. If it in not, explain why not. Name each polygon.
1.
2.
3.
4.
5. Tell whether each figure above is a regular polygon. If it is not, explain why not.
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