You must have observed that two copies of your photographs of the same size are
identical. Similarly, two bangles of the same size, two ATM cards issued by the same
bank are identical. You may recall that on placing a one rupee coin on another minted
in the same year, they cover each other completely.
Do you remember what such figures are called? Indeed they are called congruent figures (‘congruent’ means equal in all respects or figures whose shapes and sizes are both the same).
In earlier classes, you have learnt four criteria for congruence of triangles. Let us
Draw two triangles with one side 3 cm. Are these triangles congruent? Observe that they are not congruent (see Fig. 7.5).
In the above section you have studied two criteria for congruence of triangles. Let us
now apply these results to study some properties related to a triangle whose two sides
are equal. Perform the activity given below:
Construct a triangle in which two sides are equal, say each equal to 3.5 cm and the third side equal to 5 cm (see Fig. 7.24). You have done such constructions in earlier classes.
You have seen earlier in this chapter that equality of three angles of one triangle to
three angles of the other is not sufficient for the congruence of the two triangles. You
may wonder whether equality of three sides of one triangle to three sides of another
triangle is enough for congruence of the two triangles. You have already verified in
earlier classes that this is indeed true.
To be sure, construct two triangles with sides 4 cm, 3.5 cm and 4.5 cm (see Fig. 7.35). Cut them out and place them on each other. What do you observe? They cover each other completely, if the equal sides are placed on each other. So, the triangles are congruent.
In this chapter, you have studied the following points :
1. Two figures are congruent, if they are of the same shape and of the same size.
2. Two circles of the same radii are congruent.