(Q7) In the given figure if AD ⊥ BC, prove that AB² + CD² = BD² + AC².

Solution :

Given : In △ABC, AD ⊥ BC.

R.T.P : AB² + CD² = BD² + AC²

Proof : △ABD is a right angled triangle

AB² - ( )² = AD² ..... (1)

△ACD is a right angle triangle

AC² - ( )² = AD² ..... (2)

From (1) and (2)

AB² - ( )² = AC² - ( )²

AB² + ( )² = BD² + ( )²