Question

In a quadrilateral ABCD, ∠B<90⁰,AD²=AB²+BC²+CD² , prove that ∠ACD=90⁰.

Answer 1

In a quadrilateral ABCD, ∠B<90⁰,AD²=AB²+BC²+CD²

Thus it is proved that ∠ ACD = 90⁰

From figure it's clear that,

∠ B = 90°

In Δ ABC

AC^2 = AB^2 + BC^2 ..........(1)

Given,

In a quadrilateral ABCD, ∠B<90⁰,AD²=AB²+BC²+CD² ...........(2)

Combining equations (1) and (2), we get,

AD^2 = (AB^2 + BC^2) + CD^2

AD^2 = AC^2 + CD^2

Thus by using the converse Pythagoras theorem, we have,

∠ ACD = 90⁰

Therefore, it is proved that ∠ ACD = 90⁰