Fill in the blanks using the correct word given in brackets:
(i) All circles are______. (congruent, similar)
(ii) All squares are________. (similar, congruent)
(iii) All_________triangles are similar. (isosceles, equilateral)
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are________and (b) their corresponding sides are______________. (equal, proportional)

Solution:

(i) As we know that two similar figures have the same shape but not necessarily the same size. (Same size means radii of the circles are equal)

So, all circles are similar, since the radii of all the circles are not equal.

All circles are  similar  

(ii) As we know that two similar figures have the same shape but not necessarily the same size. (Same size means sides of the squares are equal.)

So, all squares are similar, since the sides of the squares are not given equal.

All squares are  similar  

(iii) An equilateral triangle has equal sides and equal angles. All equilateral triangles are similar. Each angle in an equilateral triangle is 60°.

All  equilateral  triangles are similar.

(iv) As we know that two polygons of the same number of sides are similar if their corresponding angles are equal and all the corresponding sides are in the same ratio or proportion.

1. Since the polygons have the same number of sides, we can find each angle using the formula, (2n - 4)/n right angles. Here ‘n’ is the number of sides of the polygon.
2. We can verify by comparing corresponding sides.

Two polygons of the same number of sides are similar, if (a) their corresponding angles are  equal  and (b) their corresponding sides are  corresponding  .

☛ Check: NCERT Solutions for Class 10 Maths Chapter 6

Video Solution:

Fill in the blanks using the correct word given in brackets:(i) All circles are______. (congruent, similar)(ii) All squares are________. (similar, congruent)(iii) All_________triangles are similar. (isosceles, equilateral)(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are________and (b) their corresponding sides are______________. (equal, proportional)

Class 10 Maths NCERT Solutions Chapter 6 Exercise 6.1 Question 1

Summary:

(i) All circles are similar, (ii) All squares are similar, (iii) All equilateral triangles are similar, and (iv)Two polygons of the same number of sides are similar if their corresponding angles are equal and their corresponding sides are proportional.

☛ Related Questions:

• Give two different examples of pair of (i) similar figures (ii) non-similar figures.
• State whether the following quadrilaterals are similar or not:
• In Fig. 6.17, (i) and (ii), DE || BC. Find EC in (i) and AD in (ii)
• E and F are points on the sides PQ and PR respectively of a ∆ PQR. For each of the following cases, state whether EF || QR : (i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm