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

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

3. 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.

4. 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.

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

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

7. 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

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

9. 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

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