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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles1 Mark
MCQ
In the adjoining figure, $AC= BD$. If $\angle\text{CAB} = \angle\text{DBA},$ then $\angle\text{ACB}$ is equal to:
  • A
    $\angle\text{ABC}$
  • ✓
    $\angle\text{BDA}$
  • C
    $\angle\text{ABD}$
  • D
    $\angle\text{ABC}$
✓

Answer

Correct option: B.
$\angle\text{BDA}$
In $\triangle\text{CAB}$ and $\triangle\text{DBA},$
AC = BD and $\angle\text{CAB} = \angle\text{DBA}$ (Given)
AB (Common)
Therefore, $\triangle\text{CAB}$ and $\triangle\text{DBA}$ are congruent by $SAS$ criteria
Therefore, $\angle\text{ACP} = \angle\text{BDA}$ (by $CPCT)$

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