Chapter - 5- EXERCISE 5.6 - Basic Geometrical Ideas (NCERT Class 6th Maths Solution)

1. Name the types of following triangles : 
(a) 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/Explanation:
a)Scalene triangle
b)Scalene triangle
c)Equilateral triangle
d)Right angled triangle
e)Isosceles right angled triangle
f)Acute angle 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

Solution/Explanation:

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

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


Solution/Explanation:

a)Acute angles and isosceles triangles
b)right angled and Scalene.
c)Obtuse angle and isosceles triangles
d)Right angled and isosceles triangles.
e)Acute angle and equilateral triangles.
f)Obtuse angled and Scalene.

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) Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it. 

Solution/Explanation:

a)Yes, it is possible to make a triangle of 3 matches, this is a equilateral triangle.
b)no, it is not possible to make a triangle of 4 matches, because it is not possible.
c)Yes, it is possible to make a triangle of 5 matches, this is a isosceles triangle.
d)Yes, it is possible to make a triangle of 6 matches, this is a equilateral triangle.