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RHS Theorem (Right-angle-Hypotenuse-Side)

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Please help me with the following problem:

a) Prove that two Pythagorean Triangles with the same area and equal hypotenuses are congruent.

b) Find two Pythagorean triangls with the same area.

Please show all work. Thanks in advance for the assistance.

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Solution Summary

RHS Theorem (Right-angle-Hypotenuse-Side) is applied.

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a) Suppose we have two right triangles with congruent hypotenuse's and equal areas.

I denoted both hypotenuse's by h, since they are congruent.

Now the triangles also have equal area, so .

We also have by Pythagorean's theorem that

Rearranging (1) we get , and plugging this into ...

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