MCQ
In the given fig., if $ABCD$ is a quadrilateral in which $AD = BC, AB = CD$, and $\angle\text{D} = \angle\text{B},$ then $\angle\text{CAB}$ is equal to:
- A$\angle\text{CAD}$
- ✓$\angle\text{ACD}$
- C$\angle\text{ABC}$
- D$\angle\text{BAC}$
✓
Answer
Correct option: B.
$\angle\text{ACD}$
$\angle\text{ACD}$ is the right answer;In $\triangle\text{ACD}$ and $\triangle\text{CAB}$
$AD = BC$ (Given)
$\angle\text{D}=\angle\text{B}$ (Given)
$AB = CD$ (Given)
$\therefore\triangle\text{ACD}≅\triangle\text{CAB}$ (by $SAS$ congruence criteria),
$\Rightarrow \angle\text{CAB} = \angle\text{ACD}$ (cpct).
$AD = BC$ (Given)
$\angle\text{D}=\angle\text{B}$ (Given)
$AB = CD$ (Given)
$\therefore\triangle\text{ACD}≅\triangle\text{CAB}$ (by $SAS$ congruence criteria),
$\Rightarrow \angle\text{CAB} = \angle\text{ACD}$ (cpct).
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