Question

AB = 2x DC = x + 17 AD = x + 10 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?

Answer 1

BC=2x+7

Explanation:

Answer 2

Both AB and DC are 34, the opposite sides are also congruent, thus, ABCD is indeed a parallelogram.

The length of BC is 27

Since a parallelogram has opposite sides congruent, we can equate the given side lengths to solve for BC:

We know AB = 2x and DC = x + 17. Since opposite sides are equal in a parallelogram:

AB = DC:

2x = x + 17

collect the like terms

x = 17

Find BC using the value of x:

We know BC = AD = x + 10. Substitute the value of x:

BC = AD = 17 + 10

BC = 27

To further confirm, you can also check if the other pair of opposite sides (AB and DC) is congruent:

AB = 2x = 2 × 17 = 34

DC = x + 17 = 17 + 17 = 34