 # Congruence of Triangles Class 7 Notes: Chapter 7

## Introduction to Congruent Triangles

### Congruent Figures

• Congruent figures are exactly equal in size and shape.

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### Congruent Triangles

• If all the sides and angles of a triangle are equal to the corresponding sides and angles of another triangle, then both the triangles are said to be congruent. Here, ABCDEF

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#### For More Information On Introduction To Congruent Triangles, Watch The Below Video: ## Criteria for Congruency

### SSS Criteria for Congruency

• If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.
​​​​​​​​​​​​​​ ### SAS Criteria for Congruency

• If under a correspondence, two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included between them of another triangle, then the triangles are congruent. ### ASA Criteria for Congruency

• If under a correspondence, two angles and the included side of a triangle are equal to two corresponding angles and the included side of another triangle, then the triangles are congruent. ### AAS Criteria for Congruency

AAS Rule: Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles. ### Why SSA and AAA congruency rules are not valid?

• Two triangles with equal corresponding angles need not be congruent. In such a correspondence, one of them can be an enlarged copy of the other. Therefore AAA congruency is not valid. •  If two triangles have two congruent sides and a congruent non included angle, then triangles are not necessarily congruent. Therefore, SSA congruency is not valid. ### RHS Criteria for Congruency

• If under a correspondence, the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle, then the triangles are congruent. To know more about RHS and SSS Congruency, visit here.

### Criteria for Congruency

Criteria for Congruency of two triangles are:
(i) SSS Rule
(ii) SAS Rule
(iii) ASA Rule
(iv) RHS Rule