Question

In a sight angled A the square
of hypotenuse is equal to the
Sum of squares of remaining two
sides.​

Answer 1

Answer:

Given: A right-angled triangle ABC, right-angled at B.

To Prove- AC2 = AB2 + BC2

Construction: Draw a perpendicular BD meeting AC at D.

Pythagoras Theorem Proof

Proof:

We know, △ADB ~ △ABC

Therefore, ADAB=ABAC (corresponding sides of similar triangles)

Or, AB2 = AD × AC ……………………………..……..(1)

Also, △BDC ~△ABC

Therefore, CDBC=BCAC (corresponding sides of similar triangles)

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