Question

Practice proving that a quadrilateral is a parallelogram.

Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. Line segments Z C and C X are congruent. The length of W C is 2 x + 5 and the length of C Y is 3 x + 2.

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

x =

Answer 1

x = 3

Explanation:

2x + 5 = 3x + 2

-5 -5

2x = 3x + 2 - 5

-3x -3x

2x - 3x = 2 - 5

-x = -3

x = 3