MCQ
In $\angle\text{ABC}$ and $\angle\text{DEF}, AB = DE$ and $\angle\text{A} = \angle\text{D}.$ Then, the two triangles will be congruent by $SAS$ axiom if:
- A$BC = EF$
- ✓$AC = DF$
- C$AC = DE$
- D$BC = DE$
✓
Answer
Correct option: B.
$AC = DF$
The $SAS$ rule states that:
If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
Here, in $\angle\text{ABC},$ the two sides are $AB$ and $AC$ and the included angle is $\angle\text{A}.$ For $\angle\text{DEF},$ the two corresponding sides are $DE$ and $DF$ and the included angle is $\angle\text{D}.$
Hence, the two triangles will be congruent by $SAS$ axiom if $AC = DF.$
If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
Here, in $\angle\text{ABC},$ the two sides are $AB$ and $AC$ and the included angle is $\angle\text{A}.$ For $\angle\text{DEF},$ the two corresponding sides are $DE$ and $DF$ and the included angle is $\angle\text{D}.$
Hence, the two triangles will be congruent by $SAS$ axiom if $AC = DF.$
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