Question

Define pythagoras theorem ?

Answer 1

Pythagoras Theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Proof of Pythagoras Theorem-

To Prove- AC2=AB2+BC2

For this we drop a perpendicular BD onto the side AC
We know, △ADB∼△ABC
Therefore, ADAB=ABAC (Condition for similarity)
Or, AB2=AD×AC……..(1)
Also, △BDC∼△ABC
Therefore, CDBC=BCAC (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