AB = 6x DC = x + 15 AD = 9 BC = 3y 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.

The given quadrilateral is a parallelogram.

Step-by-step explanation:

If a quadrilateral is a parallelogram, then the opposite sides would be equal.

Here we are going to equate the length of 1 pair of opposite sides to find the value of x and use this value of x to verify whether the other pair of opposite sides are equal.

AB = 6x

BC = 3x

DC = x + 15

AD = 9

Equate AB and CD,

6x = x + 15

5x = 15

x = 3

Now BC and DA should be equal.

BC = 3x = 9

Also DA = 9

As we can see, the other pair of opposite sides are also equal.

Quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent.

Hence, the given quadrilateral is a parallelogram.