AB = 3x

DC = x + 4

AD = y + 2

BC = 2y

Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Show that quadrilateral ABCD is a parallelogram by finding the lengths of the opposite side pairs.

see explanation

Step-by-step explanation:

If a parallelogram then AB = DC and AD = BC

Equating AB = DC, then

3x = x + 4 (subtract x from both sides)

2x = 4 (divide both sides by 2)

x = 2

Thus

AB = 3x = 3 (2) = 6 and DC = x + 4 = 2 + 4 = 6 ⇒ AB = DC

Equating AD and BC, then

2y = y + 2 (subtract y from both sides)

y = 2

Thus AD = y + 2 = 2 + 2 = 4 and BC = 2y = 2 (2) = 4 ⇒ AD = BC

Since opposite sides are congruent then ABCD is a parallelogram