Question

Quadrilateral ABCD is a parallelogram if its diagonals bisect each other. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 2
B) x = 3
C) x =- 9|2
D) x = -3|4

Information that goes with the picture:
AO = 5x + 2
BO = x − 1
CO = 3x − 7
DO = 3x + 8

Answer 1

Because this is a parallelogram, we know that the diagonals bisect. This means that AO = DO, and CO = BO

It doesn't matter which two segments we use, but I'm going to use CO = BO for this one.

3x - 7 = x - 1

2x = 6

x = 3

Option B. is the answer.