Question

In quadrilateral ABCD , angle A + angle B = 90° , prove that AB^2 + CD^2 = AD^2 + BD^2

Answer 1

Answer:

As ∠ABC=90

∘

So applying Pythagoras theorem in △ABC

AB

2

+BC

2

=AC

2

(1)

Given: AD

2

=AB

2

+BC

2

+CD

2

(2)

Substituting (1) in (2)

AD

2

=AC

2

+CD

2

In △ACD , applying converse of Pythagoras theorem which states

that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Hence ∠ACD=90

∘