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.
The document Congruence of Triangles Summary Class 7 NCERT Summary is a part of the Class 7 Course Mathematics Olympiad Class 7.
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