**CONTENT LIST**

## What is triangle?

Triangle is a two dimensional closed geometrical figure formed by the intersection of three lines segments . A triangle has three vertices, three sides, and three angles. The above figure shows ABC is triangle with three sides AB, BC , AC and A, B, C are the vertex and ∠ A, ∠B, ∠ C are the three angles.## Properties of a Triangle

The sum of all three interior angles of any triangle is always equal to 180⁰.

The sum of the length of any two sides of a triangle is always greater than the length of the third side.

The area of a triangle is equal to half of the product of its base and height.

## Congruent figer

If two figures that can be placed perfectly over each other, they are said to be ‘congruent’ figures.

The term “congruent” means exactly equal in shape and size.

If two objects P and Q are congruent to each other, we will write it as: P ≅ Q

## Congruent triangle

If a triangle coincides or covers the other triangle completely, then the two triangles are congruent.

AB = DE, BC = EF, AC = DF

∠A = ∠D,

∠B = ∠E,

∠C = ∠F

Here ∆ABC ≅ ∆DEF

Two triangles are called congruent if its corresponding sides and angles are equal.

The symbol of congruent is “≅”.

## Criteria for Congruence of Triangles

There are four different criteria for the two triangles to be congruent.

1.SSS (Side-Side-Side) criterion

2.SAS (Side-Angle-Side) criterion

3.ASA (Angle-Side-Angle) criterion

4.RHS (Right angle-Hypontenuse-Side) criterion

**1.SSS (Side-Side-Side) criterion**

**2.SAS (Side-Angle-Side) criterion**

**3.ASA (Angle-Side-Angle) criterion**

**4.RHS (Right angle-Hypontenuse-Side) criterion**

## Some Properties of a Triangle

**Theorem: Angles opposite to equal sides of an isosceles triangle are equal**

**Theorem: The sides opposite to equal angles of a triangle are equal.**

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