Question

AB = x + 15

AD = 2x + 18
BC = 3 - x
CD = 3x + 25
Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 3
B) x = -5
C) x = -11
D) x = 11/2

Answer 1

We have AB = CD and AD = BC;

Then, x + 15 = 3x + 25 and 2x + 18 = 3 - x;

15 - 25 = 3x - x and 2x + x = 3 - 18;

- 10 = 2x and 3x = - 15 ;

x = - 5 and x = - 5;

The correct answer is x = - 5;

B) x = - 5