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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
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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 = m S = 180 m S = 68 R S 112° T W
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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• = 70° = G 3y = 33 Then, F = 180 – 70 = 110 = H y = 11
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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 ) Given AB // DC ) Definition of a parallelogram 1 = 4, 2 = ) Alt. interior ‘s are = AB = DC ) Opposite sides of a are = ABE = CDE ) ASA AE = CE, BE = DE ) CPCTC AC and BD bisect each ) Definition of bisector other at E B C 2 4 E 1 3 A D
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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
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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 and m ADC = 6x + 84, find m BCD 3x + 11= 7x – 17 x = 7 y + 4y – 70 = 180 y = 50 2x = 6x + 84 x = 4, Angle ABC = 108, and Angle BCD = 72
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Assignment: Page 297 #1 – 12, 22, 25 – 33 odd
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