If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent. State whether the statement is true or false.

Solution:

Given, if two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent.

We have to determine if the given statement is true or false.

ASA congruence criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be congruent".

By ASA rule, it is clear that only if the two angles and the included side are equal, the triangles are congruent.

According to the question,

Two angles and one side of both the triangles are equal.

It does not imply that the included side is equal.

ASA rule does not apply in this case.

Therefore, the given two triangles are not congruent.

✦ Try This: If two sides and included angle of a triangle are equal to two sides and included angle of another triangle, then the triangles are congruent. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 102

If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent. State whether the statement is true or false.

Summary:

The given statement,”If two angles and a side of a triangle are equal to two angles and a side of another triangle, then the triangles are congruent” is false.

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