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  • “If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?

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

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[True]

Solution.         If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.

Yes, the given statement is true because by the AAS criterion of congruence, triangles are congruent.

Let us consider \triangleABC and \trianglePQR

AC = PR

\angleB = \angleQ, \angleC = \angleR

\Rightarrow \triangleABC \cong \trianglePQR

Therefore the given statement is true.

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infoexpert24

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