# Math Help - Geometrical Proof Question Help

1. ## Geometrical Proof Question Help

I am a grade 9 student, and I need help to understand how to solve these two questions. Thanks in Advance!
Also ignore the writing on the paper, it was my friends

2. ## Re: Geometrical Proof Question Help

For the 2nd problem

from the 2 right triangles you are told exist, using the pythagorean theorem

$x^2 + h^2 = a^2$

$y^2 + h^2 = b^2$

now you are told that $h^2 = x y$

substituting this in we get

$x^2 + xy = a^2$

$y^2 + xy = b^2$

adding these two equations we get

$x^2 + y^2 + 2 x y = a^2 + b^2$

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

and looking at triangle ACB we see that $x+y$ is the hypotenuse of the triangle with legs $a$ and $b$ and as

$(x+y)^2 = a^2 + b^2$ ACB must be a right triangle.

3. ## Re: Geometrical Proof Question Help

Originally Posted by pan7331
I am a grade 9 student, and I need help to understand how to solve these two questions. Thanks in Advance!
Also ignore the writing on the paper, it was my friends

for the first one just look at the right triangles caused by the fact that $BD \bot AB$ and use the pythagorean theorem.