Dimensions of two sides and one angle are provided. Two triangles are drawn using this information. Will these triangles always be congruent? Answer in Yes/No.

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Solution

Dimensions of two sides and one angle are provided.

Hence, these can be SAS or ASS order.

For SAS, any two triangles will always be congruent.

Let's take an example for ASS.

Here, length of side PR and PQ and the angle $∠ P Q R$ are fixed.

We can observe that PR can touch the base at two points $R$ and $R^{/} .$

Hence two different triangles will be obtained with the given ASS.
$∴$ This is not a criterion for congruency.

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