Use Properties of Parallelograms Section 8 – 2 Use Properties of Parallelograms

Vocabulary Parallelogram: A quadrilateral with both pairs of opposite sides parallel.

Theorem 8.3 If a quadrilateral is a parallelogram, then its opposite sides are congruent. If PQRS is a parallelogram, then 𝑃𝑄 ≅𝑅𝑆 and 𝑄𝑅 ≅𝑃𝑆.

Theorem 8.4 If a quadrilateral is a parallelogram, then its opposite angles are congruent. If PQRS is a parallelogram, then ∠𝑃≅∠𝑅 and ∠𝑄 ≅∠𝑆.

Theorem 8.5 If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. If PQRS is a parallelogram, then 𝑥°+𝑦°=180°.

Theorem 8.6 If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Example #1 Find the value of x and y. Theorem 8.4 ∠𝐹≅∠𝐻 x = 72◦ Theorem 8.3 G𝐻≅𝐾𝐹 y – 8 = 36 y = 44

Example #2 Find the measure of ∠𝑫. Theorem 8.5 ∠𝐴 𝑎𝑛𝑑 ∠𝐷 are supplementary 51◦ + 𝑚∠𝐷= 180◦ 𝑚∠𝐷= 129◦

Example #3 Find the value of each variable in the parallelogram. Theorem 8.6 diagonals bisect each other. 𝑥+3=12 𝑥=9 2𝑦−1=9 2𝑦=10 𝑦=5

Homework Section 8-2 Page 518 – 521 3 – 11, 13 – 15, 18 – 28 even, 29, 49 - 52