What is the proof of Pythagoras …
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Yogita Ingle 5 years ago
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, AD/AB = AB/AC
Now, AB2=AD×AC ..........(1)
Similarly,
BC2=CD×AC ..........(2)
Adding equations (1) and (2) we get,
AB2+BC2=AD×AC+CD×AC
=AC(AD+CD)
=AC×AC
∴AB2+BC2=AC2 [hence proved]
1Thank You