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!?

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- Nov 29th 2005, 03:06 PMrunnerforhimI'm in a hurry!!! Please help!
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!?

- Nov 29th 2005, 03:25 PMJameson
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.

- Nov 29th 2005, 04:38 PMrunnerforhimThanks...is this right?
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