Class 7 Exam  >  Class 7 Notes  >  Mathematics Olympiad Class 7  >  Summary: Congruence of Triangles

Congruence of Triangles Summary Class 7 NCERT Summary

Congruence of Plane Figures

  • If two objects are of exactly the same shape and size, they are said to be congruent and the relation between the two objects being congruent is called congruence.
  • The method of superposition examines the congruence of plane figures, line segments and angles.
  • A plane figure is any shape that can be drawn in two dimensions
  • Two plane figures are congruent, if each, when superimposed on the other, covers it exactly.

Congruence of Line Segments

  • If two line segments have the same (i.e., equal) length, they are congruent. Also, if two line segments are congruent, they have the same length.

Congruence of Angles

  • If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are same.

Congruence of Triangles

  • Two triangles are congruent if they are copies of each other and when superposed, they cover each other exactly.
  • We can tell if two triangles are congruent using 4 axioms: SAS axiom, ASA axiom, sss axiom and RHS axiom
  • SSS congruence criterion: Two triangles are congruent if three sides of one triangle are equal to the three corresponding sides of the other triangle.
  • SAS congruence criterion: Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle.
  • RHS congruence criterion: Two right-angled triangles are congruent if the hypotenuse and a side of one triangle are equal to the hypotenuse and the corresponding side of the other triangle.
  • ASA congruence criterion: Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.
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