1. 8.2 Use Properties of Parallelograms Hubarth Algebra

2. Parallelogram- is a quadrilateral with both pairs of opposite sides parallel. Theorem 8.3 P Q S R Theorem 8.4 P QR S

3. Ex 1 Use Properties of Parallelograms Find the values of x and y. ABCD is a parallelogram by the definition of a parallelogram. Use Theorem 8.3 to find the value of x. AB = CD x + 4 = 12 x =8 By Theorem 8.4, A C, or m A = m C. So, y ° = 65°.

4. Theorem 8.5 P QR S y x x y Theorem 8.6 QR S P M

5. So, m ADC + m BCD = 180°. Because m ADC = 110°, m BCD =180° –110° = 70°. By Theorem 8.5, the consecutive angle pairs in ABCD are supplementary. As shown, part of the extending arm of a desk lamp is a parallelogram. The angles of the parallelogram change as the lamp is raised and lowered. Find m BCD when m ADC = 110°. Ex 2 Use Properties of a Parallelogram

6. By Theorem 8.6, the diagonals of a parallelogram bisect each other. So, P is the midpoint of diagonals LN and OM. Use the Midpoint Formula. The correct answer is A. Ex 3 standardized Test Practice

7. Practice 1. Find FG and m G. 8, 60° 2. Find the values of x and y. 25, 15 3. NM Find the indicated measure in JKLM. 2 5. KM 4 4. m JML 70° 6. m KML 40°