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5-1 Properties of Parallelograms

- Ch. 5 Test Fri Dec. 2

Parallelogram

- A quadrilateral where both pairs of opposite

sides are parallel.

Remember your properties for parallel lines

x

z

y

- x and y are SSI angles
- Therefore, x and y are supplements
- x y 180
- x and z are also SSI therefore also supplements
- x z 180
- So, y z
- Supps of the same angle are congruent.

Theorem

x

y

- Opposite angles of a parallelogram are congruent.

(x and Y are opposite angles) - Opposite sides of a parallelogram are congruent.
- Diagonals of a parallelogram bisect each other.

Example

- Given BC 8, AB 15, EC 8, DB 18.
- Find AD
- DC
- AE
- AC
- BE
- DE

8

A

15

B

15

8

E

8

8

16

18

9

C

D

9

Example

- Given Angle ADC 82, Angle EDC 26
- Find angles
- ADE
- ABC
- EBC
- BCD
- BEC

A

B

56

82

82

56

9

E

56

56

8

8

56

98

82

98

26

56

C

D

TOOon whiteboards

- If ABCD is a parallelogram, what is the length of

segment BD? - A) 10
- B) 11
- C) 12
- D) 5

TOOon WBs

- Solve for x, y and z

12

130

10

x

y

z

Homework

- Pg. 169-170 1-12, 16 (4 steps), 19-23
- Flashcards
- Definition of Parallelogram
- 3 Theorems