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

Solution:

Given, if two sides and one angle of a triangle are equal to the two sides and angle of another triangle, then the two triangles are congruent.

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

The SAS criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are congruent.

By SAS rule, it is clear that only if the two sides and the included angle are equal, the triangles are congruent.

According to the question,

One angle of both the triangles are equal.

It does not imply that the included angles are equal.

SAS rule does not apply in this case.

Therefore, the given two triangles are not congruent.

✦ Try This: If two angles and the included side between the angles of a triangle are equal to the two angles and the included side of another triangle, then the two 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 100

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

Summary:

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

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