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5-1 Properties of Parallelograms

5-1 Properties of Parallelograms. Ch. 5 Test: Fri Dec. 2. Parallelogram. A quadrilateral where both pairs of opposite sides are parallel. x. z. Remember your properties for parallel lines. y. x and y are SSI angles Therefore, x and y are supplements x + y = 180

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5-1 Properties of Parallelograms

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  1. 5-1 Properties of Parallelograms Ch. 5 Test: Fri Dec. 2

  2. Parallelogram • A quadrilateral where both pairs of opposite sides are parallel.

  3. x z Remember your properties for parallel lines y • x and y are SSI angles • Therefore, x and y are supplements x + y = 180 • x and z are also SSI therefore also supplements x + z = 180 • So, y = z • Supps of the same angle are congruent.

  4. x Theorem y • Opposite angles of a parallelogram are congruent. (x and Y are “opposite angles”) • Opposite sides of a parallelogram are congruent. • Diagonals of a parallelogram bisect each other.

  5. Example Given: BC = 8, AB = 15, EC = 8, DB = 18. Find: AD DC AE AC BE DE 8 A 15 B 15 8 E 8 16 8 18 9 C D 9

  6. Example Given: Angle ADC = 82, Angle EDC = 26 Find angles: ADE ABC EBC BCD BEC A 56 B 82 82 9 56 E 56 56 8 8 56 98 82 98 56 26 C D

  7. B C 5 E 7 6 D A TOO—on whiteboards • If ABCD is a parallelogram, what is the length of segment BD? A) 10 B) 11 C) 12 D) 5

  8. TOO—on WBs Solve for x, y and z 12 130 10 x y z

  9. Homework • Pg. 169-170 #1-12, 16 (4 steps), 19-23 • Flashcards • Definition of Parallelogram • 3 Theorems

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