I have to prove the hypotenuse-leg congruence theorem and I have no idea how. Please help! I've triend everything, and I know you're supposed to use the pathagoeam theorem in it somewhere, but where!?
Start by drawing two triangles with six labeled sides. Then use the Pythagorean indentity to set up equations that you can use for each triangle, so as $\displaystyle a^2+b^2=c^2$ and $\displaystyle d^2+e^2=f^2$. Now say that a=d, and that c=f. Start some substituting and trying to solve for one variable that you can show will equal itself.
Ok...here's a two column proof of what I did. Is it right? A/\B (C IS THE BASE) D/\E (F IS THE BASE)
(~ means congruent)
B~E, C~F |GIVEN
A^2+B^2=C^2 |PATHAGOREAM THEOREM
A^2+E^2=F^2 |SUBSTITUTION
A^2=F^2-E^2 | SUBTRACTION
D^2=F^2-E^2 | SUBTRACTION
A^2=D^2 | TRANSITIVE
A=D | SQUARE ROOT
/\ABC~/\DEF | SSS
QED