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The Triangle and its properties-NCERT Solutions Class 7 Maths

The Triangle and its properties-NCERT Solutions Class 7 Maths, Maths NCERT solutions Class 7

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.

The Triangle and its properties-NCERT Solutions Class 7 Maths, Maths NCERT solutions Class 7

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.

The Triangle and its properties-NCERT Solutions Class 7 Maths, Maths NCERT solutions Class 7

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.

The Triangle and its properties-NCERT Solutions Class 7 Maths, Maths NCERT solutions Class 7

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

The Triangle and its properties-NCERT Solutions Class 7 Maths, Maths NCERT solutions Class 7

Watch and learn more about median and altitude – Class 7 Maths.

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.

The Triangle and its properties-NCERT Solutions Class 7 Maths, Maths NCERT solutions Class 7

 

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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December 7, 2017

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