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. What is the length of BC?

Question

Mathematics

Felipe Riley

17 April, 08:37

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. What is the length of BC?

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Answers (2)

Know the Answer?

Addisyn Morales · Answer 1

BC is the length of AD because they are parallel. Have a nice day

Xiomara Collins · Answer 2

BC is 8 units length

Step-by-step explanation:

The following information is missing in the question:

AB = 4x

CD = 2y

AD = y + 4

BC = 2y

Given that ABCD is a parallelogram, then the opposite sides are congruent. That means:

AB = CD - > 4x = 2y (eq. 1)

BC = AD - > 2y = y + 4 (eq. 2)

Solving equation 2:

2y = y + 4

2y - y = 4

y = 4

Solving equation 1:

4x = 2*4

x = 8/4

x = 2

This means that

BC = 2*4 = 8 units length

CD = 2*4 = 8 units length

AB = 4*2 = 8 units length

AD = 4 + 4 = 8 units length