Ex.6.1 Q1 Triangles Solution - NCERT Maths Class 10

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Question

 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)

  

Text Solution

   

(i) All circles are    Similar  . (congruent, similar)

Reasoning:

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)

Steps:

Similar. Since the radii of all the circles are not equal.

(ii) All squares are  Similar  . (similar, congruent)

Reasoning:

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.)

Steps:

Similar. Since the sides of the squares are not given equal.

(iii) All  Equilateral . triangles are similar. (isosceles, equilateral)

Reasoning:

An equilateral triangle has equal sides and equal angles.

Steps:

Equilateral. Each angle in an equilateral triangle is \({{60}^{{}^\circ }}\).

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

Reasoning:

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

Steps:

(i) Since the polygons have same number of sides, we can find each angle using formula \(\begin{align}\left( {\frac{{2n - 4}}{n}} \right)\end{align}\) right angles. Here \(‘n’\) is number of sides of a polygon.

(ii) We can verify by comparing corresponding sides.

 

  
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