## 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.

*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.*

__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**

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

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