In a quadrilateral ABCD, Angle B=90 degree, AD²=AB²+BC²+CD².

Prove that Angle ACD=90 degree.

Question

In a quadrilateral ABCD, Angle B=90 degree,
AD2=AB2+BC2+CD2
Prove that Angle ACD=90 degree

Ankush Jain · Accepted Answer

Given: ABCD is a quadrilateral,
âˆ B = 90Â° and AD2 =
AB2 + BC2 + CD2

To prove: âˆ ACD =
90Â°

Proof: In right âˆ†ABC,

AC2 = AB2 + BC2
â€¦ (1)

Given, AD2 = AB2 + BC2 +
CD2

â‡’ AD2 = AC2 +
CD2 (Using (1)

In âˆ†ACD,

AD2 = AC2 + CD2

âˆ´ âˆ ACD = 90Â°
(Converse of Pythagoras theorem)

In a quadrilateral ABCD, Angle B=90 degree, AD2=AB2+BC2+CD2. Prove that Angle ACD=90 degree.