MCQ
If $\triangle\text{ABC}$ and $ \triangle\text{DBC}$ are on the same base $BC, AB = DC$ and $AC = DB$ (figure). then which of the following gives a congruence relationship?
  • A
    $\triangle\text{ABC}\cong\triangle\text{DBC}$
  • B
    $\triangle\text{ABC}\cong\triangle\text{CBD}$
  • $\triangle\text{ABC}\cong\triangle\text{DCB}$
  • D
    $\triangle\text{ABC}\cong\triangle\text{BCD}$

Answer

Correct option: C.
$\triangle\text{ABC}\cong\triangle\text{DCB}$

Since, $AB = DC$ [given]
and $AC = DB [common base]$
$BC = BC$
By $SSS$ congruence criterion, $\triangle\text{ABC}\cong\triangle\text{DCB}$

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