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Sorting Quadrilaterals Activity

From Geometry Teacher’s Activity Workbook p 114 & 115

1a. Remove the Concave quadrilaterals? Which did you remove?

3. 6.

1b. The Rest…2. 4. 5.

9. 10.

13.

15. 16.

12. 14.

1.

7. 8.

11.

2. 4. 5.

9. 10.

13.

15. 16.

1.

7. 8.

11. 12. 14. 12. 14.

2. Which of these have no parallel sides?

Remove them from your stack.

2. 4. 5.

9. 10.

13. 15. 16.

7. 8.

3. Which of the remaining quadrilaterals have 1 pair of parallel sides?1. 1.

7. 8.

Remove them from your stack.11. 11.

4. Which of the remaining quadrilaterals have 2 sets of parallel sides?

2. 4. 5. 9.

10. 13. 15. 16.

2. 4. 5. 9.

10. 13. 15. 16.

5. Which of the parallelograms have 4 right angles?

2. 4. 5. 9.

10. 13. 15. 16.

4. 5.

10. 15.

6. Which of the rectangles have 4 congruent sides?

4. 5.

10. 15.

5.

15.

7. Collect all of the parallelograms. Which of the parallelograms have 4 congruent sides?

2. 4. 5. 9.

10. 13. 15. 16.

5. 9.

15. 16.

Parallelograms

Sec: 8.2

Sol: G.8 a, b, c

Foldable

1. Take out a piece of notebook paper and make a hot dog fold over from the right side over to the pink line.

Foldable

2. Now, divide the right hand section into 5 sections by drawing 4 evenly spaced lines.

The fold crease

3. Use scissors to cut along your drawn line, but ONLY to the crease!

Foldable

4. Write QUADRILATERALS down the left hand side

The fold crease

Foldable

5. Fold over the top cut section and write PARALLELOGRAM on the outside.

The fold crease

6. Reopen the fold.

Foldable

7. On the left hand section, draw a parallelogram.

1. Opposite angles are congruent.

2. Consecutive angles are supplementary.

3. Opposite sides are congruent.

4. Diagonals bisect each other.

5. Diagonals make 2 congruent triangles.

8. On the right hand side, list all of the properties of a parallelogram.9. Place in your notebook and save for tomorrow.

ParallelogramParallelogramIs a quadrilateral with both pairs of opposite sides

parallel.Ex:

What are the vertices?

Symbol: ABCD *they are labeled in order as they appear starting with one vertice.

QuadrilateralsQuadrilateralsAre four-sided polygons.

What is a polygon? PolygonsExample: Non – example:

Example: Give the possible names of the following figure.

D

A C

B

Properties of ParallelogramsTheorem 8-3 : Opposite sides of a

parallelogram are congruent. Ex:

Theorem 8-4 : Opposite angles in a parallelogram are congruent.

D

A B

C

If AD = 16, BC=_______If AB = 25, DC = _______

D

A B

C

If the mA = 100, then m C = _____If the mD = 80, then mB = ______

Theorem 8-5 : Consecutive angles in a parallelogram are supplementary.

Theorem 8-6 : If a parallelogram has one right angle, it has four right angles.

D

A B

C

If mA = 120, then mB =_________If mA = 120, then mC =_________If mC = 120, then mD =_________

A

D C

B mA = 90 mB= 90 mC = 90 mD = 90

Theorem 8-7 : Diagonals of a parallelogram: The diagonals of a parallelogram bisect each other. Meaning the intersection of the two diagonals is the midpoint of each diagonal.

Theorem 8-8 : Each Diagonal of a parallelogram separates the parallelogram into two congruent triangles.

D

A B

C

If AM = 16, MC = ___If DM = 25, MB = ___If AC = 30, MC = ___

M

D

A B

C

CABACD

Example:1. MATH is a parallelogram. Find w, x, y and z.

H

M A

T

w° y°

55° z°

Example:2. Solve for w, x, y, and z.

S

C A

R

3x - 4

17.

9

4w - 3

11.13z –

3

15.

4

20

2y +

5

38°

33°

Example:3. Parallelogram STOP has

diagonals , that intersect at point M. If SM = 3a + 18, SO = 12a, MT = a+2b, MP = 3b + 1. Find a. b. and TP.

TPandSO