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ABCD is a parallelogram.

E is the point where the diagonals AC and BD meet.

Prove that triangle ABE is congruent to triangle CDE.

Charlie
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    Use https://www.algebra.com/algebra/homework/Parallelograms/prove-that-the-diagonals-of-parallelogram-bisect-each-other-.lesson – lab bhattacharjee Apr 30 '17 at 13:20
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    The angles are all equal (trivial geometry) so they are similar and therefore scalable to each other. And the corresponding sides are equal by the property of a parallelogram so the scale is one. Done. – Deepak Apr 30 '17 at 13:23

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AE and EC are on the same line, so have the same gradients. Same goes for BE and ED. Because it is a parallelogram, AB=CD, as it has to be so that the shape holds. Therefore, you have proved this by the Angle-Side-Angle rule, where two triangles with two identical angles and a side are congruent, even if they are reflected.

If you know the gradient, and set the known side to 0 degrees, the gradient shows the vector, which is also an angle.

Xetrov
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