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.
    Congruent Triangles
    Here, ABCDEF

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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.
    ​​​​​​​​​​​​​​SSS Criteria for Congruency

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.
    SAS Criteria for Congruency

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.
    ASA Criteria for Congruency

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.
AAS Criteria for Congruency

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.
    Why SSA and AAA congruency rules are 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.

Why SSA and AAA congruency rules are 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.
    RHS Criteria for Congruency

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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 180° 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 ‘Angle sum property’?

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

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.

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