Question

prove Pythagoras theorem​

Answer 1

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Answer 2

hi mate,

Pythagoras 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.