7.2 Parallelograms

Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Consecutive angles Opposite angles

Properties of parallelograms: 1. opposite sides are congruent 2. opposite angles are congruent 3. diagonals bisect each other 4. consecutive angles are supplementary

How could you prove that a quadrilateral is a parallelogram? 1) Show both pairs of opposite sides are parallel 3) Show both pairs of opposite angles are congruent 4) Show one pair of opposite sides is congruent and parallel 5) Show that the two diagonals bisect each other 2) Show both pairs of opposite sides are congruent

The diagonals of a parallelogram bisect each other and form 2 pairs of congruent triangles.

1. Find the missing angles. 50° 60° 40°

(2y – 3) 2. Find the value of y 23

16 4m + 4 3c + 9 9c -3 Ex 3. Find the length of each diagonal.

A H 4. Find the coordinates of point R T M R

Example 4: Find the values of x & y in KLMN N M L K X 5y 2 equations, 2 unknowns: 5y = 2x + 5 x = 7y y = 2(7y – 16) + 5 5y = 14y – y = -27 y = 3 x = 7y – 16 x = 7(3) – 16 x = 21 – 16 x = 5 2x + 5 7y - 16

5. Given quadrilateral ABCD, with vertices A (0,0), B(2,4), C(7,4), and D(5,0), prove that ABCD is a parallelogram.