Page 187 - ICSE Math 7

17 Congruence of Triangles

Key Concepts

• Congruent Figures • Congruence of Triangles
• Congruence of Line Segments • Conditions for Congruency of Two Triangles
• Congruence of Two Angles

There are a lot of things around us with the same shape and size like
table tennis balls of the same brand, coins of the same denomination,
mobile phones of the same model and colour etc. They are congruent
to each other. Similarly, there are congruent triangles also. They have
wide applications in the real world. You must have enjoyed a ride on
a giant wheel. Can you identify the congruent triangles in it?
Look at the cable bridge in the adjoining figure. Cables are attached
to each pillar on both sides to form congruent triangles to balance the
weight of the roadway.

Congruent Figures

In geometry, when two geometrical figures cover exactly each other,
i.e., they have same size and shape, we say the figures are congruent
or they are in congruence.
Two plane figures having same shape need not be congruent. For two figures to be congruent, they
must have same size as well. To check congruency, we take a trace-copy of one of them and place it
on the other. If the two figures cover each other exactly, they are congruent. This method of comparing
two figures is called the method of superposition. Congruency of figures is denoted by the symbol
≅. Let’s consider some examples.

The two pairs of figures shown above are congruent as they have same shape and size and each one
of them fits into the other exactly.

Congruence of Line Segments

Two line segments are said to be congruent if and only if they have the same length.

A B C D
Symbolically, we write AB ≅ CD if and only if AB = CD.

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