derive pyrhagoream identities??? han?

Question

my teacher asked me to derive the Pythagorean theorem?
i dont realy know how to do it?
can someone help?

Answer 1

There are many proofs of the Pythagorean Theorem, but the classic and elegant proof is the one performed by Pythagoras over 2000 years ago. It is extremely long but it's logic is beautiful. You can find it on the internet if you search for Euclid's Elements.

But a much simpler proof is as follows:
Draw a rt triangle ACB with C being the right angle and AB being the hypotenuse. Now draw an altitude from C to AB at D.
Then BC^2=(AB-AD)AB {Reason 1: In a right triangle, with an altitude drawn to the hypotenuse, the (leg)^2 = adjacent segment times the hypotenuse}
BC^2 = AB^2 -AB*AD {distributive property}
AC^2 = AD*AB {Same as Reason 1}
AC^2 + BC^2 = AB^2 +AD*AB-AD*BD {Addition property}
AC^2 +BC^2 = AB^2 (algebra)

Answer 2

Its all in here:

http://www.themathpage.com/aTrig/proof.htm