Question

AB = x + 4 DC = 12 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?

Answer 1

AB = DC = 12

AD = BC = 10

Explanation:

For ABCD to be a parallelogram, opposite side pairs must be congruent. That will be the case when ...

AB = DC

x+4 = 12 . . . . substitute expressions for length

x = 8 . . . . . . . subtract 4

Then the lengths of AD and BC must be ...

BC = AD = x+2 = 8+2 = 10

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The figure will be a parallelogram when x=8 and sides have lengths ...

AB = DC = 12

AD = BC = 10

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Comment on the problem

Of course, if x ≠ 8, or BC ≠ AD, the figure will not be a parallelogram. You are asked to show the figure IS a parallelogram, but all you can really show is that the figure CAN BE a parallelogram. In order to do anything useful with the given expressions for side lengths, you must assume the figure is a parallelogram.