# Class 6 Triangle

Isosceles Right-Angle Triangle

## Triangle

If P, Q, R are three non-collinear points, the figure made up by three line segments PQ, QR and RP is known as triangle with P, Q and R as vertices.

We shall use the symbol △ PQR to denote the triangle. The three line segments PQ, QR and RP are called the sides of the triangle.

The three angles ∠RPQ , ∠PQR, and ∠QRP are known as angles of the triangle. We can denote this angles as ∠P, ∠Q and ∠R respectively.

There are various types of tringles as mentioned below.

- Equilateral Triangle
- Isosceles Triangle
- Scalene Triangle
- Acute Triangle
- Right Triangle
- Zero angle
- Obtuse Triangle
- Isosceles Right-Angle Triangle

## Equilateral Triangle

A triangle whose all sides are equal is known as equilateral triangle.

## Isosceles Triangle

A triangle whose two sides are equal is known as isosceles triangle.

## Scalene Triangle

A triangle whose no two sides are equal is known as scalene triangle.

## Acute Triangle

A triangle whose each angle is less than 90° is known as acute triangle.

## Right Triangle

A triangle whose one angle is equal to 90° is known as right angled triangle or right triangle.

## Obtuse Triangle

A triangle whose one angle is more than 90° is known as obtuse triangle.

## Isosceles Right-Angle Triangle

A triangle whose one angle is equal to 90° and it's two sides are equal then it is known as isosceles right angle triangle.

## Perimeter of a triangle

The sum of the lengths of the sides of a triangle is known as it's perimeter.

**Example 1.** Find the perimeter of the below triangle.

**Solution.** PQ = 5cm, PR = 4 cm and QR = 7 cm

Perimeter = PQ + PR + QR

= 5 + 4 + 7 = 16 cm

So, the perimeter of the triangle is 16 cm.

**Example 2.** Find the perimeter of the below triangle.

**Solution.** XY = 3cm, YZ = 5 cm and ZX = 5 cm

Perimeter = XY + YZ + ZX

= 3 + 5 + 5 = 13 cm

So, the perimeter of the triangle is 13 cm.

## Properties of Triangle

1. If all the angles in a triangle are equal, then its sides are equal.

2. If all the sides of a triangle are equal, then angles are also equal.

3. If two angles of a triangle are equal, then it has two equal sides.

4. If two sides of a triangle are equal, then its two angles are also equal.

5. If none of the angles of a triangle are equal, then none of the sides are equal.

6. The sum of all the angles of a triangle is equal to 180°.

7. The sum of lengths of any two sides is greater than the length of the third side.

## Class-6 Triangle Test

## Class-6 Triangle Worksheet

## Answer Sheet

**Triangle-Answer**Download the pdf

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