Congruence of Triangles Class 7 Notes: Chapter 7

Introduction to Congruent Triangles

Congruent Figures

  • Congruent figures are exactly equal in size and shape.

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

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

Criteria for Congruency

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

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