Question

Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent show that quadrilateral ABCD is a parallelogram by finding the length of the opposite side pairs

Answer 1

D. 21, 14

Explanation:

As the question said, a parallelogram is formed when both pairs of opposite sides are congruent. That means that 21 and 3y are equal, as are y + 7 and 2y.

21 = 3y

/3 /3

7 = y

y + 7 = 2y

-2y -2y

-y + 7 = 0

- 7 - 7

-y = -7

* -1 * -1

y = 7

In both instances, y = 7. Now let's substitute that.

21 = 3(7)

21 = 21 is true.

7 + 7 = 2(7)

14 = 14 is true.

With that, the lengths of the opposites sides are 21 & 14, which is D.