Lesson 8 2 Parallelograms Lesson 6 1 Parallelogram

Lesson 8 -2 Parallelograms Lesson 6 -1: Parallelogram 1

Parallelogram Definition: A quadrilateral whose opposite sides are parallel. B Symbol: a smaller version of a parallelogram C D A Naming: l A parallelogram is named using all four vertices. l You can start from any one vertex, but you must continue in a clockwise or counterclockwise direction. l For example, the figure above can be either ABCD or ADCB. Lesson 6 -1: Parallelogram 2

A Properties of Parallelogram D B P 1. Both pairs of opposite sides are congruent. 2. Both pairs of opposite angles are congruent. 3. Consecutive angles are supplementary. 4. Diagonals bisect each other but are not congruent Lesson 6 -1: Parallelogram C 3

B A Properties of Parallelogram D C 5. If a parallelogram has one right angle, it has four right angles. 6. Each diagonal of a parallelogram separates the parallelogram into two congruent triangles. Lesson 6 -1: Parallelogram 4

H Examples 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. P K M L Draw HKLP. HK = _______ and HP = ____. m<K = m<______. m<L + m<______ = 180. If m<P = 65 , then m<H = ____, m<K = ______ and m<L =____. Draw the diagonals with their point of intersection labeled M. If HM = 5, then ML = ____. If KM = 7, then KP = ____. If HL = 15, then ML = ____. If m<HPK = 36 , then m<PKL = _____. Lesson 6 -1: Parallelogram 5

K H Examples M L P 11. ΔLMH is congruent to which other Δ? _____ 12. <HLP is supplementary to ______ Use the following information HK=3 y, LP=18, m<HPL =18, And m<HPK = 40. 13. Find m<LHP ____________ 14. Find m<HKP ____________ 15. Find y. ______________ Lesson 6 -1: Parallelogram 6