MCQ
In Fig , if $A C=B D$ and $\angle C A B=\angle D B A$, then $\angle A C B=$
- A$\angle B A D$
- B$\angle A B C$
- C$\angle A B D$
- D$\angle B D A$
✓
Answer
D. $\angle B D A$
In triangles $A B C$ and $A B D$, we have
$
A B=A B
$$\quad$[Common]
$\angle C A B=\angle D B A$$\quad$[Given]
and,$\quad$$
A C=B D
$$\quad$[Given]
So, by $S A S$ congruence criterion,
we obtain$
\triangle A B C \cong \triangle B A D \Rightarrow \angle A C B=\angle B D A
$
In triangles $A B C$ and $A B D$, we have
$
A B=A B
$$\quad$[Common]
$\angle C A B=\angle D B A$$\quad$[Given]
and,$\quad$$
A C=B D
$$\quad$[Given]
So, by $S A S$ congruence criterion,
we obtain$
\triangle A B C \cong \triangle B A D \Rightarrow \angle A C B=\angle B D A
$
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