MCQ
In Fig , if $A B=F C, E F=B D$ and $\angle A F E=\angle C B D$. Then, the rule by which $\triangle A F E \cong \triangle C B D$ is
- ASAS
- BASA
- CSSS
- DAAS
✓
Answer
A. SAS
We have,
$
A B=F C \Rightarrow A B+B F=B F+F C \Rightarrow A F=B C
$
Thus, in triangles $A F E$ and $C B D$, we obtain
$
\begin{aligned}
A F & =B C \\
\angle A F E & =\angle C B D \\
and, F E & =B D
\end{aligned}
$
So, by $S A S$ congruence criterion, we obtain $\triangle A F E \cong \triangle C B D$.
We have,
$
A B=F C \Rightarrow A B+B F=B F+F C \Rightarrow A F=B C
$
Thus, in triangles $A F E$ and $C B D$, we obtain
$
\begin{aligned}
A F & =B C \\
\angle A F E & =\angle C B D \\
and, F E & =B D
\end{aligned}
$
So, by $S A S$ congruence criterion, we obtain $\triangle A F E \cong \triangle C B D$.
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