# Math՚s: Congruence: Congruence of Triangles, and Criteria for Congruence of Triangles (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Congruence

Two figures, which have the same shape and same size are called congruent figures and this property is called congruence.

Congruent figures, when placed one over another, exactly coincide with one another or cover each other. In other words, two figures will be congruent, if parts of one figure are equal to the corresponding parts of the other.

• Two-line segments are congruent if they are of equal length
• Two polygons are equal if they have same number of sides and all of their sides are equal or their areas are equal
• Two circles are congruent if their radii are equal.

## Congruence of Triangles

Two triangles are congruent, if all the sides and all the angles of one are equal to the corresponding sides and angles of other.

• For Example, in the above triangles, we can say, PQR is congruent to XYZ and we write
• Congruence of two figures also implies that their corresponding (matching) parts are also equal. In the above triangles, P corresponds to X, Q corresponds to Y and R corresponds to Z. Also, and .

## Criteria for Congruence of Triangles

In order to prove the congruence of two triangles, we are required to prove the equality of any of the three of their corresponding parts. Some of the Important criteria for proving the congruence of two triangles are-

• SAS (Side- Angle- Side) Criteria- If any two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle, the two triangles are congruent.
• In the following pair of triangles ABC and PQR, and . So, by SAS criteria.