1. SSS Congruence

Congruent figureS 
    Figures having same shape and size are called congruent figures. 
    Two figures are congruent if each is an exact image of the other. E.g. coins of M5.

Concept of superimposition 
    If two figures are congruent, then without bending or changing their position, if one figure is placed over the other figure and they completely overlap each other, then two figures are said to be superimposed on each other. 

•     Two figures are congruent if one figure superimposes the other figure.

If triangle T₁ superimposes triangle T₂ and these two figures exactly cover each other, then they are called congruent. This method is also called superimposition method.

Chapter 7

Congruence of Triangles

Real-life examples of congruent objects

There are infinite examples of congruent objects which we see or observe in our daily life. A simple example is a pack of biscuits with all biscuits of the same size and shape if they are not broken. We can say all the biscuits are congruent.
A few more examples of congruency are:

• Earrings of the same set.
• Cigarettes in a pack.
• Wheels of a bicycle.
• Pages of a particular book.
• Your little fingers of both hands. Other fingers and thumbs are also congruent. Many of your body organs, like kidneys and lungs, are congruent. Even if a body is cut vertically from the center into two halves, both halves are congruent.

SSS Congruence

Congruence of triangles: Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is’ ≅’.
The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size. 
Congruence is the term used to define an object and its mirror image. Two objects or shapes are said to be congruent if they superimpose on each other.
The meaning of congruent in Maths is addressed to those figures and shapes that can be repositioned or flipped to coincide with the other shapes. These shapes can be reflected to coincide with similar shapes.
Congruent Triangles
A closed polygon made of three line segments forming three angles is known as a Triangle.
Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle.

In the above figure, Δ ABC and Δ PQR are congruent triangles. This means,
Vertices:  A and P, B and Q, and C and R are the same.
Sides:  AB=PQ, QR= BC and AC=PR;
Angles:  ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.

SSS Congruence Rule (Side – Side – Side)
The triangles are said to be congruent if all the three sides of one triangle are equal to the three corresponding sides of another triangle

Example :

In the given triangles ABC and PQR, AB = 3.5 cm, BC = 7.1 cm, AC = 5 cm, PQ = 7.1 cm, QR = 5 cm and PR = 3.5 cm. Examine whether the given two triangles are congruent or not. If yes, then write the congruence relation in symbolic form.

Solution :

Given : AB = PR = 3.5 cm
BC = PQ = 7.1 cm and
AC = QR = 5 cm
This shows that all the sides of one triangle are equal to all sides of the other triangle. By using SSS congruence rule, the two triangles are congruent. From the three equality relations, we can write it as 

 A↔R, B↔P, C↔Q
So, the congruence of triangles in symbolic form is ∆ABC ≅ ∆RPQ