# 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 trianglesÂ are said to be congruent.

Here, â–³ABCâ‰…â–³DEF

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## 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.
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### 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.
• Â 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.

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### Criteria for Congruency

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

## Frequently asked Questions on CBSE Class 7 Maths Notes Chapter 7: Congruence of Triangles

### What are some of the facts of triangles?

A triangle has: 1. three sides, three vertices and three angles 2. The sum of the three interior angles of a triangle is always 180Â° 3. The sum of the length of two sides of a triangle is always greater than the length of the third side.

### What is the â€˜Angle sum propertyâ€™?

The angle sum property of a triangle says that the sum of its interior angles is equal to 180Â°.

### What are some of the uses of triangles?

Triangles can be used to make trusses. Trusses are used in many structures, such as roofs, bridges and buildings.