Well-designed AP 6th Class Maths Textbook Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.6 offers step-by-step explanations to help students understand problem-solving strategies.
Understanding Elementary Shapes Class 6 Exercise 5.6 Solutions – 6th Class Maths 5.6 Exercise Solutions
Question 1.
Name the types of following triangles:
a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
Solution:
Lengths of the sides of a triangle are given as : 7 cm, 8 cm and 9 cm
Since, all sides of the given triangle are different.
Hence, it is a scalene triangle.
b) △ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
Solution:
Given that, AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
Here AB ≠ AC ≠ BC
Hence, △ABC is a scalene triangle.
c) △PQR such that PQ = QR = PR = 5 cm.
Solution:
Given that, PQ = QR = PR = 5 cm
Since all sides are equal
Hence, It is an equilateral triangle.
d) △DEF with m∠D = 90°.
Solution:
Given that, in △DEF, m∠D = 90°.
Hence, it is a right angled triangle.
e) △XYZ with m∠Y = 90° and XY = YZ.
Solution:
Given that, in △XYZ, m∠Y = 90° and XY = YZ .
Hence, it is isosceles right angled triangle.
f) △LMN with m∠L = 30°, m∠M = 70° and m∠N = 80°
Solution:
Given that, △LMN, m∠L = 30°, m∠M = 70° and m∠N = 80°
Hence, it is an acute angled triangle,
Question 2.
| 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 |
Solution:
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 the angle by observation)
Solution:
a) i) Acute angled triangle
ii) Isosceles triangle
b) i) Right angled triangle
ii) Scalene triangle
c) I) Obtuse angled triangle
iV) Isosceles triangle
d) i) Right angled triangle
ii) Isosceles triangle
e) i) Acute angled triangle
ii) Equilateral triangle
f) i) Obtuse angled triangle
ii) Scalene triangle
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.
