Question

In the above figure, $DE=DF,DE\perp AB,DF\perp AC$ then which of the following is true?

• A. $\angle EDB=\angle FDC$
• B. $\angle DBE=\angle DCF$
• C. $\angle ADE=\angle ADF$

Answer 1

The correct option is C $\angle ADE=\angle ADF$

Taking triangles,
$△DEAand△DFA$
$\angle DEA=\angle DFA={90}^o\left(Given\right)$
$AD=AD$ (Common Side in both triangles)
$DE=DF$ (Given)
So,$△DEA\cong △DFA\left(RHS\right)$

We know, corresponding angles of congruent triangles are equal,
Hence, $\angle ADE=\angle ADF$
and $\angle DAF=\angle DAE$