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Given ABCD is a parralelogram choose and label approproate coordinates for A, B, C, and D, and prove that the opposite sides of ABCD are congruent. point A is (0,0) point B is (10,0) point C is (12,7) and point D is (3,7)

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Answer:

proved: see explanation below

Explanation:

The parallelogram ABCD has cordinates point A is (0,0) point B is (10,0) point C is (12,7) and point D is (3,7).

For the opposite sides of ABCD to be congruent, the slope of the opposite sides would be equal

If AB // CD, BC // AD, it’s a parallelogram.

If slope of AB = CD, BC = AD then it’s a parallelogram.

slope = Δy/Δx

slope AB = (0-0)/(10-0) = 0

slope BC = (7-0)/(12-10) = 7/2

slope CD = (7-7)/(12-3) = 0

slope DA = (0-7)/(0-3) = 7/3

slope DA is supposed to be equal to slope BC

It means the coordinate of D is (2,7)

slope DA becomes= (0-7)/(0-2) = 7/2

Therefore it would be proved that the opposite sides of ABCD are congruent as two pair of slopes are equal

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