6-2 Properties of Parallelograms 1/26/17 Objective: To relate sides, angles, diagonals, and transversals of parallelograms THEOREM 6-1 Opposite sides of a parallelogram are congruent

CONSECUTIVE ANGLES: angles of a polygon that share a side Ex: Find m S in RSWT. R and S are consecutive angles of a parallelogram. They are supplementary (S.S.I.A) m R + m S = 180 112 + m S = 180 m S = 68 R S 112° T W

Opposite angles of a parallelogram are congruent THEOREM 6-2 Opposite angles of a parallelogram are congruent Find the value of y in EFGH. Then find m E, m G, m F, and m H F G 3y + 37° 6y + 4° E H 6y + 4 = 3y + 37 3y + 4 = 37 So, E = 6•11 + 4 = 70° = G 3y = 33 Then, F = 180 – 70 = 110 = H y = 11

The diagonals of a parallelogram bisect each other THEOREM 6–3 The diagonals of a parallelogram bisect each other Proof of THEOREM 6-3 Given: ABCD Prove: AC and BD bisect each other at E Statements Reasons ABCD is a parallelogram 1) Given AB // DC 2) Definition of a parallelogram 1 = 4, 2 = 3 3) Alt. interior ‘s are = AB = DC 4) Opposite sides of a are = ABE = CDE 5) ASA AE = CE, BE = DE 6) CPCTC AC and BD bisect each 7) Definition of bisector other at E B C 2 4 E 1 3 A D

THEOREM 6-4 If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal BD = DF A B C D E F

A B P Parallelogram ABCD D C If AB = 3x + 11 BC = 2x + 19 CD = 7x – 17 Find x If m BAD = y and m ADC = 4y – 70, find y If m ABC = 2x + 100 and m ADC = 6x + 84, find m BCD 3x + 11= 7x – 17 x = 7 y + 4y – 70 = 180 y = 50 2x + 100 = 6x + 84 x = 4, Angle ABC = 108, and Angle BCD = 72

Assignment: Page 297 #1 – 12, 22, 25 – 33 odd