In and , = , = , = , then by which congruence rule ? - Vidyadip

MCQ

In $\triangle\text{AOC}$ and $\triangle\text{XYZ},\ \angle\text{A}=\angle\text{X},\ \angle\text{AO} = \angle\text{XY},\ \angle\text{AC} = \angle\text{XZ},$ then by which congruence rule $\triangle\text{AOC}\cong\triangle\text{XYZ}?$

A
$RHS$
✓
$SAS$
C
$ASA$
D
$SSS$

✓

Answer

Correct option: B.

$SAS$

According to $SAS$ criterion, if the corresponding sides and their included angles are equal, then the triangles are congruent. Here, in $\triangle\text{AOC}$ and $\triangle\text{XYZ},$ $AO = XY$, and $AC = XZ$ are the corresponding sides and $\angle\text{A}=\angle\text{X}$ are included angles, Hence, $\triangle\text{AOC}\cong\triangle\text{XYZ},$ by $SAS.$

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