Class 10 RD Sharma Solutions – Chapter 4 Triangles – Exercise 4.1

Question 1. (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, equilaterals) :
(iv) Two triangles are similar, if their corresponding angles are _____________(proportional, equal)
(v) Two triangles are similar if their corresponding sides are _____________ (proportional, equal)
(vi) 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) All circles are Similar

ii) All squares are Similar

iii) All Equilateral triangles are similar

iv) Two triangles are similar if their corresponding angles are Equal

v) Two triangles are similar if their corresponding sides are Proportional

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

Question 2. Write the truth value (T/F) of each of the following statements :

(i) Any two similar figures are congruent.
(ii) Any two congruent figures are similar.
(iii) Two polygons are similar if their corresponding sides are proportional.
(iv) Two polygons are similar if their corresponding angles are proportional.
(v) Two triangles are similar if their corresponding sides are proportional.
(vi) Two triangles are similar if their corresponding angles are proportional.

Solution:

i) False, as in some cases similar polygons can be congruent too.

ii) True

iii) False, as their corresponding angles must also be equal.

iv) False, as angles are equal but not congruent.

v) True

vi) True

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