Question

If DH = 2x – 2 and FH = x + 6, find the value of x for which DEFG must be a parallelogram.

Answer 1

x=8

Explanation:

Given that DEFG is a parallelogram.

H is the centre of the parallelogram where diagonals meet.

Since diagonals bisect each other,

DH = FH

2x-2 =x+6

Solving we get

x =8

DEFG is a parallelogram.

Answer 2

We have to find the value of x for which DEFG must be a parallelogram.
Point H is the center of the parallelogram DEFG. Therefore: DH = FH2 x - 2 = x + 62 x - 2 + 2 = x + 6 + 22 x = x + 82 x - x = x - x + 8Answer:
x = 8