Exercise 5.6

Class 6 | Mathematics | Chapter 5| Understanding Elementary Shapes | Exercise 5.6

1. Name the types of following triangles :

(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.

(b) ΔABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) ΔPQR such that PQ = QR = PR = 5 cm.(d) ΔDEF with m ∠D = 90°
(e) ΔXYZ with m ∠Y = 90° and XY = YZ
(f) ΔLMN with m ∠L = 30°, m ∠M = 70° and m∠N = 80°.

Answer:

(a) Scalene triangle

(b) Scalene triangle

(c) Equilateral triangle

(d) Right-angled triangle

(e) Isosceles right-angled triangle

(f) Acute-angled triangle

2. Match the following :
Measures 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

Answer :

(i) : (e)

(ii) : (g)

(iii) : (a)

(iv) : (f)

(v) : (d)

(vi) : (c)

(vii) : (b)

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

Answer:

(a) Acute angled triangle and Isosceles triangle

(b) Right-angled triangle and scalene triangle

(c) Obtuse-angled triangle and Isosceles triangle

(d) Right-angled triangle and Isosceles triangle

(e) Equilateral triangle and acute angled triangle

(f) Obtuse-angled triangle and scalene triangle

4. Try to construct triangles using sticks. Some are shown here. 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.

Answer:

(a) 3 matchsticks This is an acute angle triangle and it is possible with 3 matchsticks to make a triangle because sum of two sides is greater than third side.

(b) 4 matchsticks This is a square, hence with four matchsticks we cannot make triangle.

(c) 5 matchsticks This is an acute angle triangle and it is possible to make triangle with five matchsticks, in this case sum of two sides is greater than third side.

(d) 6 matchsticks This is an acute angle triangle and it is possible to make a triangle with the help of 6 matchsticks because sum of two sides is greater than third side.