Question

Given altitudes in ABC. What additional information is needed to prove $△AFD\cong △BFE$ ?

• A. $AC\cong BC$
• B. $AE\cong BD$
• C. $AB\cong BC$
• D. $DF\cong BC$

Answer 1

The correct option is B $AE\cong BD$

In $△AFD$ and $△BFE$

$\angle AFD\cong \angle BFE$ ..... (Opposite angles formed by lines $AE,DB$)

If it's given that $AE\cong BD$

Then,

$AF\cong FB$ and $FD\cong EF$

Then by $SAS$ postulate $△AFD$ and $△BFE$ are congruent.

Hence, $AE\cong BD$ is needed to prove the congruency of triangles.