In the given figure, $\angle A B C$ and $\angle A C B$ are complementary to each other and $A D \per

Question

In the given figure, $\angle A B C$ and $\angle A C B$ are complementary to each other and $A D \perp B C$. Then,\

Professor PC Thomas Classes · Answer

(c): We have, \[By angle sum property]\ From (i) and (ii), we get, $\angle A C B=\angle B A D$\ In $\triangle A D C$ and $\triangle B D A$\ $\angle A D C=\angle B D A=90^{\circ}$\ $\angle A C D=\angle B A D$\ [Proved above]\ $\therefore \quad \triangle A D C \sim \triangle B D A$\ [By AA similarity]\ $\therefore \quad \frac{A D}{B D}=\frac{C D}{A D} \Rightarrow A D^{2}=B D \cdot C D$ \ Concept Applied - Two angles are complementary to each other, if the sum of both angles is $90^{\circ}$.