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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