1. Properties of Parallelograms
Section 7.2

2. What You Will Learn
Use properties to find side lengths and angles of parallelograms.
Use parallelograms in the coordinate plane.

3. Using Properties of Parallelograms

5. Parallelogram Opposite Sides Theorem

6. Using Properties of Parallelograms
Find the values of x and y.

7. You Try

9. Parallelogram Diagonals Theorem

10. Using Properties of a Parallelogram
As shown, part of the extending arm of a desk lamp is a parallelogram. The angles of the parallelogram change as the lamp is raised and lowered. Find m∠BCD when m∠ADC = 110°.

11. Writing a Two-Column Proof

12. Using Parallelograms in the Coordinate Plane
Find the coordinates of the intersection of the diagonals of ▱LMNO with vertices L(1, 4), M(7, 4), N(6, 0), and O(0, 0).

13. Using Parallelograms in the Coordinate Plane
Three vertices of ▱WXYZ are W(−1, −), X(−3, 2), and Z(4, −4). Find the coordinates of vertex Y. 3

14. You Try
Find the coordinates of the intersection of the diagonals of ▱STUV with vertices S(−2, 3), T(1, 5), U(6, 3), and V(3, 1).
Three vertices of ▱ABCD are A(2, 4), B(5, 2), and C(3, −1). Find the coordinates of vertex D.

15. CRITICAL THINKING
Points W(1, 2), X(3, 6), and Y(6, 4) are three vertices of a parallelogram. How many parallelograms can be created using these three vertices? Find the coordinates of each point that could be the fourth vertex.