# The Triangle and its properties NCERT Solutions Class 7 Maths

## Triangle and its properties-NCERT Solutions Class 7 Maths

Class 7 Maths – Chapter 6 – Triangle and its properties Introduction

A plane figure surrounded by three line segments is called a triangle. It is donated by the symbol . So if we talk about ∆ABC it has

• Three vertices, namely A, B, and C.
• Three sides namely AB, BC, and CA.
• Three angles namely ∠A,B, and ∠C.

A triangle has six parts – 3 sides and 3 angles.

Types of triangle

We know that triangle can be classified on the basis of sides and angles.

Based on Sides

• Scalene triangle
• Isosceles triangle
• Equilateral triangle

Based on Angles

• Acute angled
• Obtuse-angled
• Right angled triangle

Maths NCERT solutions of Class 7 are available at Class 7 Maths.

Medians of a triangle

The line segment joining the mid-point of a line segment BC of a triangle to its opposite vertex A is called median of the triangle.

A median connects a vertex of a triangle to the mid-point of the opposite side.

In the above triangle ABC, AE is the median of the side BC.

CD is the median of the side AB

BF is the median of the side AC

Altitudes of a triangle

An altitude has one endpoint at a vertex of the triangle and the other on the line containing the opposite side. Through each vertex of a triangle, an altitude can be drawn.

Below is the figure which will represent median and altitude in the single triangle.

Exterior angle of a triangle and its properties

An exterior angle of a triangle can be formed by extending the sides of a triangle at its vertex. A triangle can have three exterior angles.

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

Proof:-

Given – Consider ∆ABC

∠ACD is an exterior angle

To Show:-

M ∠ACD=m ∠A +m ∠B

Through C draw CE parallel to BA

∠1= ∠X (BA is parallel to CE and AC is a transversal so the alternate angle should be equal)

∠2= ∠y (BA is parallel to CE and AD is a transversal so the corresponding angle should be equal)

∠1+ ∠2= ∠x+ ∠y

As we know ∠x+ ∠y=m ∠ACD

So, ∠1+ ∠2= ∠ACD

Hence proved

The above relation proved between an exterior angle and its two interior opposite angles are referred as the exterior angle property of a triangle.

For examples and practice questions click on CBSE Class 7th Maths.

## You can read more topics of Maths NCERT Solutions Class 7

Lines and Angles

Triangle and its properties

We will discuss the angle sum property of the triangle in the next article.

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August 23, 2019