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8-2: Parallelograms

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.

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8-2: Parallelograms

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  1. 8-2: Parallelograms

  2. 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 D C

  3. 8-2: Parallelograms • In parallelogram PQRS, PQ = 20, QR = 15, and mS = 70 • Find SR and SP • SR is opposite PQ, so SR = 20 • SP is opposite QR, so SP = 15 • Find mQ • Q is opposite S, so Q = 70 • Find mP • S and P are supplementary • S + P = 180 • 70 + P = 180 • P = 110 Q P S R

  4. 8-2: Parallelograms • Your Turn • In parallelogram DEFG, DE = 70, EF = 45, and G = 68 • Find GF • 70 • Find DG • 45 • Find mE • 68 • Find mF • 112

  5. 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 E A D B C Congruent becauseof SSS A D

  6. 8-2: Parallelograms • Assignment • Worksheet #8-2

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