Congruence of Triangles Class 7 Notes: Chapter 7

According to the CBSE Syllabus 2023-24, this chapter has been removed from NCERT Class 7 Maths textbook.

Introduction to Congruent Triangles

Congruent Figures

• Congruent figures are exactly equal in size and shape.

To know more about Congruent Figures, visit here.

Congruent Triangles

• If all the sides and angles of a triangle are equal to the corresponding sides and angles of another triangle, then both triangles are said to be congruent.
  
  Here, $△ABC\cong △DEF$

To know more about the Congruence of Triangle, visit here.

For more information on The 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 are SSA and AAA congruency rules 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 the Congruency of two triangles are:
(i) SSS Rule
(ii) SAS Rule
(iii) ASA Rule
(iv) RHS Rule