8-2: Parallelograms

8-2: Parallelograms PARALLELOGRAM: A quadrilateral with two

pairs of parallel sides

Theorems about parallelograms Theorem 8-2: Opposite angles of a parallelogram

are congruent. Theorem 8-3: Opposite sides of a parallelogram

are congruent. Theorem 8-4: Consecutive angles of a

parallelogram are supplementary.

A B

C D

8-2: Parallelograms In parallelogram PQRS, PQ = 20, QR = 15, and mS = 70 Find SR and SP

SR is opposite PQ, so SR = 20 SP is opposite QR, so SP = 15

Find mQ Q is opposite S, so Q = 70

Find mP S and P are supplementary S + P = 180 70 + P = 180 P = 110

P Q

RS

8-2: Parallelograms YOUR TURN

In parallelogram DEFG, DE = 70, EF = 45, and G = 68 Find GF

70 Find DG

45 Find mE

68 Find mF

112

8-2: Parallelogram Theorem 8-5: The diagonals of a

parallelogram bisect each other.

Theorem 8-6: A diagonal of a parallelogram separates it into two congruent triangles

B C

A D

E

BE EDAE EC

B C

A D

Congruent becauseof SSS

ABD CBD

8-2: Parallelograms Assignment

Worksheet #8-2