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1.Let $\triangle ABC$ be a right triangle, with the point $H$ the foot of the altitude from $C$ to side $\overline{AB}$.

Prove that

Jan 31, 2019
edited by Guest  Jan 31, 2019
edited by Guest  Jan 31, 2019

#1
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Look under your first post regarding question No. 1.

Jan 31, 2019
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(x+ h)^2 + (y + h)^2 = (a + b)^2       expand

x^2 + 2xh + h^2 + y^2 + 2yh + h^2 = a^2 + 2ab + b^2

By the Pythagorean Theorem.....

(x^2 + h^2) + ( y^2 + h^2)  = a^2 + b^2

So....we have left that

2xh + 2yh   =  2ab

xh + yh = ab

h (x + y) = ab       multiply both sides by 1/2

(1/2) (x + y)  * h =  (1/2)ab

Since this is a right triangle    (1/2) product of legs a, b  = the area of ABC = the right side

And the left side is (1/2)base of ABC * height = the area of ABC

So...the left side = the right side

Jan 31, 2019