Question

in a quadrilateral abcd angle b is 90 degree. if ad ^2 equal to ab^2 +bc ^2+cd^2, than prove that angle acd is 90 degree

Answer 1

Given: ABCD is a quadrilateral, ∠B = 90° and AD2 = AB2 + BC2 + CD2
To prove: ∠ACD = 90°
Proof: In right ∆ABC,
AC2 = AB2 + BC2 … (1)
Given, AD2 = AB2 + BC2 + CD2
⇒ AD2 = AC2 + CD2 (Using (1)
In ∆ACD,
AD2 = AC2 + CD2
∴ ∠ACD = 90° (Converse of Pythagoras theorem)