Geometry 5 1 Properties of Parallelograms Defn of

Geometry 5. 1 Properties of Parallelograms

Defn. of a Parallelogram A quadrilateral with both pairs of opposite sides parallel A B In D C ABCD, AB DC and AD BC

Theorem Opposite sides of a parallelogram are congruent.

Theorem Opposite angles of a parallelogram are congruent.

Theorem Diagonals of a parallelogram bisect each other.

All figures are ||-ograms) 1. 2. 3. a+b y x 3 a+2 b 30 12 x = ____ y = ____ 4. 5. y+10 2 y 2 a = ____ b = ____ 80 x 2+2 x 8 x = ____ y = ____ 6. 26 x 11 x -4 x-3 4 y+5 4 x+2 y 20 5 y 2+16 45 80 x = ____ y = ____ 6 y+16 x = ________ y = ________ 24 y x 2

Homework pg. 168 CE #1 -13 odd pg. 169 WE #5 -12, 19 -29

Think about why this theorem is true A B 4 1 2 <1 <2 <3 <4 DB DB Alt. int. <‘s 3 D C Reflexive Apply youare know about the properties of parallel The twowhat triangles congruent by ASA. Corresponding parts are congruent. lines. AD CB CPCTC AB CD CPCTC

Again, this theorem is true by applying what you know about parallel lines and congruent triangles. A D B <B <D <A <C C <B and <D are made up of two pairs of congruent alt. int. <‘s (add small angles together using Angle Addition Postulate) <A and <C are congruent because CPCTC

This theorem is true using previous theorems Black ∆ Red ∆ by ASA CPCTC

From the Homework Turn to pg. 169 #8, #22, #26