# Leg squared theorem

• Jun 1st 2014, 11:36 AM
jgolden1
Leg squared theorem
I took notes in class on this theorem, but still don't understand how to do it. Can someone explain how this works/what to do? Attachment 31054
• Jun 1st 2014, 12:18 PM
Plato
Re: Leg squared theorem
Quote:

Originally Posted by jgolden1
I took notes in class on this theorem, but still don't understand how to do it. Can someone explain how this works/what to do? Attachment 31054

What you have are three similar right triangles. The tedious part is figuring the correct correspondences.
Here is one \$\Delta ACB \simeq \Delta ADC\$ .
Can you find two more?
Then read off the corresponding proportionals and cross multiply.
• Jun 1st 2014, 12:19 PM
Shakarri
Re: Leg squared theorem
You can prove \$\displaystyle h^2=xy\$ by using pythagoras' theorem for the big triangle and the two smaller triangles.
and you can prove that \$\displaystyle a^2=yc\$ and \$\displaystyle b^2=xc\$ by using \$\displaystyle h^2=xy\$ and pythagoras' theorem for the smaller triangles