Question

AB = 2x + 61

BC = 60 − 3x
CD = 6x + 45
AD = 40 + 2x

Quadrilateral 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) 65 cm, 44 cm
B) 69 cm, 48 cm
C) 76 cm, 52 cm
D) 80 cm, 58 cm

Answer 1

B) 69 cm, 48 cm

Step-by-step explanation: The way to get the answer is by making AB equal to CD because when you draw the parallelogram, they are congruent. Once you solve for x (equals 4) in 2x + 61 = 6x + 45 you substitute x in 2(4) + 61 and get 69. Now you substitute x in AD: 40 + 2x. You get 48. You dont need to substitute in BC because it is parallel to AD, meaning it is congruent. Now with the 2 answers, you get 69 cm for AB and CD, and you get 48 cm for BC and AD. Hope this helped.