In a quadrilateral ABCD, ∠B=90∘. If AD2=AB2+BC2+CD2, prove that ∠ACD=90∘.
Answer:
- Given: A quadrilateral ABCD in which ∠B=90∘ and AD2=AB2+BC2+CD2.
- Here, we have to prove that ∠ACD=90∘.
Now, join AC.
In ΔABC, ∠B=90∘. ∴ AC2=AB2+BC2… (i) [By Pythagoras' theorem] Now ,AD2=AB2+BC2+CD2⟹AD2=AC2+CD2[ using(i)] Thus, in ΔACD, we have AD2=AC2+CD2.
Hence, ∠ACD=90∘[ By converse of pythagoras' theorem ].