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

Guest Jan 31, 2019

edited by
Guest
Jan 31, 2019

edited by Guest Jan 31, 2019

edited by Guest Jan 31, 2019

#2**+2 **

(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

CPhill Jan 31, 2019