NCERT Solutions for Class 6 Maths Chapter 5 Exercise 5.3

Class VI Mathematics Ex. 5.3 of chapter 5 Understanding Elementary Shapes free in Hindi and English Medium updated for session 2024-25. Get here the videos related to all the questions given in class 6 mathematics exercises 5.3. We have used simple steps to solve the questions, so that students can understand easily each math sum. Contents are free to use in Tiwari Academy App and websites.

A plane figure formed by three non-parallel line segments is called a triangle.
If P, Q and R, are three non-collinear points in the plane, then the figure made up by three line segments PQ, QR and RP is called a triangle with vertices P, Q and R.
We use the symbol PQR to denote the triangle PQR with vertices P, Q and R. Image

The three line segments PQ, QR and RP, that form the triangle PQR are called the sides of the triangle.
The three angles ∠PQR, ∠QRP and ∠QPR are called the angles of the triangle PQR. For the sake of convenience, we denote angles ∠QPR, ∠PQR and ∠QRP by ∠P, ∠Q and ∠R respectively.
The six parts, namely three sides and three angles of a triangle taken altogether are called the six elements of the triangle.

Note: In a triangle, two sides always include an angle and two angles always include a side. Each pair of two sides has a vertex in common.

In triangle PQR, we observe that the sides PQ and PR meet at vertex P and QR is the remaining side. So, we say that ‘QR’ is the side opposite to vertex P and P is the vertex opposite to side QR. Similarly, RP is the side opposite to vertex Q and Q is the vertex opposite to side RP. Also, PQ is the side opposite to ∠R and ∠R is the angle opposite to side PQ. Clearly, PQ is the side opposite to vertex R and R is the vertex opposite to side PQ.

Draw a triangle KLM on a sheet of paper.
We see that it divides all the points of the plane into three parts:

1. The part of the plane which consists of all points such as P, is called the interior of the triangle
2. The part of the plane which consists of all points such as R, forms the triangle itself.
3. The interior of the triangle KLM, together with the triangle, is called the triangular region KLM
4. The part of the plane which consists of all points such as Q, is called the exterior of the triangle.
5. We observe that we cannot go from P to Q or from Q to P without crossing a side of the triangle.

Triangles are named on the basis of the lengths of their sides and the measures of their angles as given below:
Naming Triangles by Considering the Lengths of Their Sides.

A triangle in which all the three sides are unequal in length is called a scalene triangle.

A triangle in which two sides are equal in length is called an isosceles triangle.

A triangle in which all the three sides are equal in length is called an equilateral triangle.

Right-Angled Triangle:
A triangle in which one angle is right angle, i.e., equal to 90° is called a right-angled triangle.

Acute-Angled Triangle:
A triangle in which each of the three angles is acute, i.e., less than 90° (right angle) is called an acute-angled triangle.

Obtuse-Angled Triangle:
A triangle in which one angle is obtuse, i.e., more than 90° (right angle) is called an obtuse-angled triangle.

(i) An equilateral triangle is an acute-angled triangle and the measure of its each angle is 60°.
(ii) The two angles in each case of right-angled and obtuse-angled triangles are acute.
(iii) In an isosceles-triangle, two angles are equal.

The sum of the angles of a triangle is 180° or 2 right angles. As a consequence of the above result, we can say that:

• (i) A triangle cannot have more than one right angle.
• (ii) A triangle cannot have more than one obtuse angle.
• (iii) In a right angled triangle, the sum of the two acute angles is 90°.