# Triangles -CBSE CLASS 9

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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

SSS (Side-Side-Side) criterion states If three sides of any triangle are equal to the three sides of another triangle, then these two triangles are congruent.

2.SAS (Side-Angle-Side) criterion

SAS (Side-Angle-Side) criterion states two triangles are congruent, if two sides and the included angle of a triangle are equal to the two sides and the included angle of the other triangle

3.ASA (Angle-Side-Angle) criterion

ASA (Angle-Side-Angle) criterion states two triangles are congruent, if two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle.

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

RHS (Right angle-Hypontenuse-Side) criterion states If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent

## 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.

Related Topics

• Polynomials: Chapter Note
• Coordinate Geometry: Chapter Note
• Linear equation in two variables: Chapter Note
• Euclids Geometry: Chapter Note
• Lines and angles: Chapter Note