Question

“If two sides and an angle of one triangle are equal to two sides and an angle of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

• A. True
• B. False

Answer 1

The correct option is B False

Verify the statement.

The Side angle side(SAS) congruency says that if two sides and the angle included by the two sides are equal to the corresponding two sides and angle of the other triangle then the triangles are congruent.

The angle must be the included the side.

Let's take an example.

We have two triangle $∆ABC$ and $∆PQR$.

Where, $AB=PQ,$ $AC=PR$ and $\angle ABC=\angle PQR$

We can see how the side can be rotated out $\left(AC\to PR\right)$ to form a larger triangle.

Thus we can say that two sides and a non-include angles are not enough information to guarantee two triangles will be congruent.

Hence, the given statement is false.