Question

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.

Answer 1

see explanation

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

Answer 2

6,4

Explanation: