Question

State and prove Pythagoras theorem ​

Answer 1

Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given: ABC is a triangle in which ∠ABC=90

Construction: Draw BD⊥AC.

Proof:

In △ADB and △ABC

∠A=∠A [Common angle]

∠ADB=∠ABC [Each 90∘ ]

△ADB∼△ABC [A−A Criteria]

So, ABAD = ACAB

Now, AB 2 =AD×AC ..........(1)

Similarly,

BC 2 =CD×AC ..........(2)

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

AB 2+BC 2 =AD×AC+CD×AC=AC(AD+CD)=AC×AC

∴AB

Hence Proved.

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