Understanding Elementary Shapes-Solutions Ex-5.6

CBSE Class –VI Mathematics
NCERT Solutions
Chapter 5 Understanding Elementary Shapes (Ex. 5.6)

Question 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 mD = 90
(e)ΔXYZ with mY = 90 and XY = YZ
(f)ΔLMN with mL = 30,mM = 70 and mN = 80.
Answer:  (a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Right-angled triangle
(e) Isosceles right-angled triangle
(f) Acute-angled triangle
Question 2. Match the following:
Measure of Triangle
Types of Triangle
(i)3 sides of equal length
(a) Scalene
(ii) 2 sides of equal length
(b) Isosceles right angle
(iii) All sides are of different length
(c) Obtuse angle
(iv) 3 acute angles
(d) Right angle
(v) 1 right angle
(e) Equilateral
(vi) 1 obtuse angle
(f) Acute angle
(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)
Question 3. Name each of the following triangles in two different ways: (You may judge the nature of 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
Question 4. Try to construct triangles using match sticks. 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)
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.