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Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the
(a) RHS congruence criterion
(b) ASA congruence criterion
(c) SAS congruence criterion
(d) AAA congruence criterion

Solution:

Given, two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle.

We have to find the type of congruence criterion.

(i) RHS - RightAngle-Hypotenuse-Side rule

RHS congruence theorem states that, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent.

(ii) ASA - Angle-Side-Angle congruence rule

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".

(iii) SAS - Side-Angle-Side congruence rule

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.

(iv) AAA - Angle-Angle-Angle congruence rule

Angle-Angle-Angle congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.

Therefore, the required congruence criterion is ASA.

✦ Try This: In a triangle ABC, ∠B = 26° and ∠C = 56°. Find ∠A

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 45

Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the: (a) RHS congruence criterion, (b) ASA congruence criterion, (c) SAS congruence criterion, (d) AAA congruence criterion

Summary:

Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the ASA congruence criterion.

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