Page 184 - Start Up Mathematics_7

11 Congruence of Triangles

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.

In this chapter, we will learn about congruency of plane figures only.

Congruent Figures

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 said to be 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.

Case I: Case II:

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 iff they have the same length.

A B C D
Symbolically, we write AB  CD iff AB = CD.