1. Date: Topic: Properties of Parallelograms (7.1) Warm-up Find x and the missing angle measures The angles of a triangle add up to 180 degrees. 3x + 4x + 2 + 4x + 2 = 180 11x + 4 = 180 -4 11x = 176 11 x = 16 3(16) = 4(16) + 2 = (4x+2)° 66° 48°

2. Definition of a Parallelogram A parallelogram is a quadrilateral that has two pairs of parallel sides. Opposite angles are two angles that do not share a common side. Opposite angles of ABCD: and Opposite sides are two sides that do not share a common endpoint. Opposite sides of ABCD: and A parallelogram is a quadrilateral (4 sided polygon), so its angles add up to 360°.

3. d Properties of Parallelograms Opposite sides are equal in length. Opposite angles are congruent. The diagonals bisect each other. 10 x 15 y x =10 y =15 a b a = b = 6 7 c c = d = 6 7 Consecutive angles are supplementary. 6 7 15 10

4. Find the missing angle measures. x y z Opposite angles of a parallelogram are congruent. The angles of a triangle add up to 180 degrees. -150° -142° Also… Alternate Interior Angles of parallel lines (opposite sides of the parallelogram) and a Transversal (the diagonal) are congruent.

5. Find x and y. 25 3x+10 The diagonals of a parallelogram bisect each other. 3x+10 = 25 -10 3x = 15 3 3 x = 5 4y - 3 21 4y – 3 = 21 + 3 4y = 24 44 y = 6