Help please (GEOMETRY)

Question

AB = 4x

DC = 16

AD = y + 4

BC = 2y

1) 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. A) 12, 4

B) 12, 8

C) 16, 4

D) 16, 8

Answer 1

So, in order to solve this, you must set the opposite sides to equal each other. That means AB=CD and BC=AD, which means 4x=16 and 2Y=Y+4. Solving for x, you get x=16/4, by dividing both sides by 4, which equals x=4. Plugging x=4 back into the measurements of the sides, you get that AB & CD both equal 16. Solving for Y, you get Y=4, by subtracting Y from both sides, and then plugging y=4 back into the original sides, you get that both BC & AD equal 8. So the answer is D.