Question

AB = x + 20

DC = 5x
AD = x − 2
BC = ?

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?
A) 2
B) 3
C) 6
D) 9

Answer 1

BC=3 units

Explanation:

Parallelograms

We are told that quadrilateral ABCD is a parallelogram because both pairs of opposite sides are congruent. This means AB=CD. We also know

`AB = x + 20`

`DC = 5x`

`AD = x - 2`

Using the condition AB=CD

`x + 20=5x`

`4x=20`

`x=5`

Knowing the value of x, we can say

`AD = x - 2=3`

BC must be equal to AD

`BC=3\ units`

We can see AB=5+20=25, and that DC=5(5)=25. All pairs of opposite sides are congruent