Question

In $\Delta ABC$ and $\Delta DEF$, $AB=FD$, $\angle A=\angle D$. The two triangles will be congruent by SAS axiom if :

• A. $BC=DE$
• B. $AC=EF$
• C. $BC=EF$
• D. $AC=DE$

Answer 1

Answer: (D)

$AC=DE$

For the triangles to be congruent by $SAS$ axiom we need two sides and included angle of given triangles to be equal.

Given: $AB=FD$ and $\angle A=\angle D$

Now from the figures, we can say that we need the second pair of sides which is $AC$ and $DE$ according to the given definition.

So for given triangles to be congruent by $SAS$ criteria

we need $AC=DE$

Option $D$ is correct.