NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6 are the part of NCERT Solutions for Class 6 Maths (Rationalised Contents). Here you can find the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.1
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.2
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.3
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.7
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.8

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6 (Rationalised Contents)

Ex 5.6 Class 6 Maths Question 1.

Name the types of following triangles:
(а) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) ∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) ∆PQR such that PQ = QR = PR = 5 cm.
(d) ∆DEF with m∠D = 90°.
(e) ∆XYZ with m∠Y = 90° and XY = YZ.
(f) ∆LMN with m∠L = 30°, m∠M = 70° and m∠N = 80°.

Solution:
(a) The lengths of the three sides of a triangle are given as: 7 cm, 8 cm and 9 cm.
Since, all the sides of the given triangle are different.
Hence, it is a scalene triangle.
(b) Given in a ∆ABC, AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
Here, AB ≠ AC ≠ BC. Hence, ∆ABC is a scalene triangle.
(c) Given in PQR, PQ = QR = PR = 5 cm.
Since all the sides of the triangle are equal.
Hence, it is an equilateral triangle.
(d) Given in ∆DEF, m∠D = 90°.
Hence, it is a right-angled triangle.
(e) Given in ∆XYZ, m∠Y = 90° and XY = YZ.
Hence, it is an isosceles right-angled triangle.
(f) Given in ∆LMN, m∠L = 30°, m ∠M = 70° and m∠N = 80°.
Hence, it is an acute-angled triangle.

Ex 5.6 Class 6 Maths Question 2.

Match the following:
Measure of triangle Type of triangle
(i) 3 sides of equal length (a) Scalene
(ii) 2 sides of equal length (b) Isosceles right angled
(iii) All sides are of different length (c) Obtuse angled
(iv) 3 acute angles (d) Right angled
(v) 1 right angle (e) Equilateral
(vi) 1 obtuse angle (f) Acute angled
(vii) 1 right angle with two sides of equal length (g) Isosceles

Solution:
(i) ↔ (e)
(ii) ↔ (g)
(iii) ↔ (a)
(iv) ↔ (f)
(v) ↔ (d)
(vi) ↔ (c)
(vii) ↔ (b)

Ex 5.6 Class 6 Maths Question 3.

Name each of the following triangles in two different ways: (You may judge the nature of the angle by observation)

Solution:
(a) (i) Acute-angled triangle or (ii) Isosceles triangle

(b) (i) Right-angled triangle or (ii) Scalene triangle

(d) (i) Right-angled triangle or (ii) Isosceles triangle

(e) (i) Acute-angled triangle or (ii) Equilateral triangle

(f) (i) Obtuse-angled triangle or (ii) Scalene triangle

Ex 5.6 Class 6 Maths Question 4.

Try to construct triangles using matchsticks. Some are shown here. Can you make a triangle with
(a) 3 matchsticks?
(b) 4 matchsticks?
(c) 5 matchsticks?
(d) 6 matchsticks?

(Remember you have to use all the available matchsticks in each case)
Name the type of triangle in each case.
If you cannot make a triangle, think of reasons for it.

Solution:
(a) Yes, we can make an equilateral triangle with 3 matchsticks.

(b) No, we cannot make a triangle with 4 matchsticks.
(c) Yes, we can make an isosceles triangle with 5 matchsticks.

(d) Yes, we can make an equilateral triangle with 6 matchsticks.