# Triangles and Its Properties Class 7 Notes: Chapter 6

## Introduction

### Triangle

• A triangle is a closed curve made of three line segments.
• It has three:Sides:
(i) Sides: Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯AB, Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯BC and Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯CA
(ii) Angles: âˆ BAC, âˆ ACB and âˆ CBA
(iii) Vertices: A, B and C

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## Important Lines in a Triangle

### Median

• Median is the line that connects a vertex of a triangle to the mid-point of the opposite side.
• In the given figure, Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯AD is the median, joining the vertexÂ A to theÂ midpoint of Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯BC.

### Altitude

• An altitude is a line segment throughÂ a vertex of the triangle and perpendicular to a line containing the opposite side.

## Sides Also Have Constraints

### Sum of the lengths of two sides of a triangle

• The sum of the lengths of any two sides of a triangle is greater than the third side.

In the above triangle,
9+11=20 >14
11+14=25 >9
9+14=23 >11

### Difference between lengths of two sides of a triangle

• The difference between lengths of any two sides is smaller than the length of the third side.
• In the above triangle,
11 – 9 = 2 < 14
14 – 11 = 3 < 9
14 – 9 = 5 < 11
• Using the concept of sum of two sides andÂ difference of two sides, it is possible to determine the range of lengths that the third side can take.

## Triangle Properties

### Angle sum property of a triangle

• The total measure of the three angles of a triangle is 1800.
• In â–³PQR,
âˆ RPQ+âˆ PQR+âˆ QRP
=700Â + 600Â + 500Â = 1800

#### For More Information On Angle Sum Property Of A Triangle, Watch The Below Video.

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### Exterior angle of a triangle and its property

• An exterior angle of a triangle is equal to the sum of its interior opposite angles.

In the given figure, âˆ 1+âˆ 2=âˆ 3.

### Pythagoras Theorem

• The side opposite to the right angle in a right-angledÂ triangle is called the hypotenuse.
• The other two sides are known as legs of the right-angled triangle.
• In a right-angled triangle, square ofÂ hypotenuse is equal to the sum ofÂ squares ofÂ legs.

AC2=AB2+BC2
â‡’52=42+32
• If a triangle holdsÂ Pythagoras property, then it is a right-angled triangle.

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### Properties of isosceles and equilateral triangles

Properties of Isosceles TriangleÂ

• Two sides are equal in length.
• Base angles opposite to the equal sides are equal.

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Properties of Equilateral Triangle

• All three sides are equal in length.
• Each angle equals to 600.

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## Classification of Triangles

### Classification of triangles based on sides

• Equilateral triangle: A triangle in which all the three sides are of equal lengths.
• Isosceles triangle: A triangle in which two sides are of equal lengths.
• Scalene Triangle: A triangle in which all three sides are of different length.

### Classification of triangles based on angles

• Acute-angled: A triangle with three acute angles.
• Right-angled: A triangle with one right angle.
• Obtuse-angled: A triangle with one obtuse angle.

## Frequently asked Questions on CBSE Class 7 Maths Notes Chapter 6: Triangles and its Properties

### What are some of the facts of triangles?

A triangle has: 1. three sides, three vertices and three angles 2. The sum of the three interior angles of a triangle is always 180Â° 3. The sum of the length of two sides of a triangle is always greater than the length of the third side.

### What is the â€˜Angle sum propertyâ€™?

The angle sum property of a triangle says that the sum of its interior angles is equal to 180Â°.

### What are some of the uses of triangles?

Triangles can be used to make trusses. Trusses are used in many structures, such as roofs, bridges and buildings.