Question

proof pythagorus theorum

Answer 1

in a right angle the square of the length of the hypotenuse is equal to the sum of the square of the length of legs there are several methods to prove the Pythagorean theorem......

given triangle ABC prove that a2 +b2=c2 .

first construct a perpendicular from C to AB

Answer 2

lPythagoras Theorem Proof

Given: A right-angled triangle ABC.

To Prove- AC² = AB² + BC²

Proof: First, we have to drop a perpendicular BD onto the side AC

We know, △ADB ~ △ABC

Therefore,

AD AB

----- = -----

AB AC

(Condition for similarity)

Or, AB² = AD × AC …………………..……..(1)

Also, △BDC ~△ABC

Therefore,

CD BC

----- = -----

BC AC

(Condition for similarity)

Or, BC²= CD × AC …………………………..(2)

Adding the equations (1) and (2) we get,

AB² + BC² = AD × AC + CD × AC

AB² + BC² = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC² = AB² + BC²

Hence, the Pythagorean thoerem is proved.