geometry honors

Can you prove ABCD is a parallelogram based on the given information? Explain.
Given: x = 5, y = 4
Prove: ABCD is a parallelogram.

The image consists of a quadrilatera ABCD with their sides AB, BC, CD, DA as 3x + 12, 7y - 8, 6x - 3 and 5y respectively.

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1. To be a ||gm , opposite sides must be equal
7y-8 = 5y and 6x-3 = 3x+12

7y - 8 = 5y
2y = 8
y = 4

6x-3 = 3x+12
3x = 15
x = 5

Since the given information about x and y match those solutions, yes, it is a parallogram

or

just sub in the given values into the 4 different expressions to see that indeed opposite sides are equal

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posted by Reiny

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