Question

in a quadrilateral ABCD angle=90 Prove that​

Answer 1

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∘

Step-by-step explanation:

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