AB = 44 + 3xBC = 33 + yCD = 64 - xAD = 48 - 2yQuadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Prove that quadrilateral ABCD is a parallelogram by finding the lengths (in centimeters) of the opposite side pairs? A) 51 cm, 30 cmB) 55 cm, 33 cmC) 59 cm, 38 cmD) 64 cm, 42 cm

The lengths (in centimeters) of the opposite side pairs are 59 cm, 38 cm. Option C) is the correct answer.

Step-by-step explanation:

step 1:

Given that,

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

step 2:

The opposite sides are AB and CD respectively.

The another opposite sides are BC and AD respectively.

step 3:

If both pairs of opposite sides are congruent, then

AB = CD

44+3x = 64-x

3x+x = 64-44

4x = 20

x = 5

step 4:

BC = AD

33+y = 48-2y

y+2y = 48-33

3y = 15

y = 5

step 5:

Subsitute x=5 and y=5 in any of the given sides,

CD = 64-x = 64-5 = 59

∴ CD = 59 cm

BC = 33+y = 33+5 = 38

∴ BC = 38 cm

The lengths of the opposite side pairs are 59 cm, 38 cm.