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.

step-by-step explanation:

10

step-by-step explanation:

7+3=10