Triangles ⇒⇒ Exercise 6.1

Question 1 (i)

Fill In the b1ank using the correct word given in brackets:
(i) All circles are _______ . (congruent, similar)

Solution :

(i) All circles are _similar .

( As we know that two similar circles have the same shape (Round), but not necessarily the same size. They may have different radius but the shape of all circles is the same.)

Hence, These circles are similar but not congruent.

Question 1 (ii)

Fill In the b1ank using the correct word given in brackets:
(ii) All squares are _______. (similar, congruent)

Solution :

(ii) All squares are _similar .

( As we know that two similar squares have the same shape , but not necessarily the same size. They may have a different sides of the squares but the shape of all square is the same..)

Hence, These squares are similar but not congruent.

Question 1 (iii)

Fill In the b1ank using the correct word given in brackets:
(iii) All ______ triangles are similar. (isosceles, equilateral)

Solution :

(ii) All _equilateral triangles are similar.

Isosceles Triangle :

Equilateral Triangle :

( Since all the equilateral triangles have a similar shape, and sides are in same ratio in equilateral triangle.)

Hence, all equilateral triangles are similar.

Question 1 (iv)

Fill In the b1ank using the correct word given in brackets:
(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 :

(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.

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

Question 2 (i)

Give two different examples of pair of
(i) similar figures

Solution :

(i) similar figures

Pair of rectangles with different breadth and length.

Pair of circles with different radii.

Question 2 (ii)

Give two different examples of pair of
(ii) non-silimar figures.

Solution :

(ii) non-silimar figures.

Trapezium and square.

Triangle and parallelogram

Question 3

State whether the following quadrilaterals are similar or not:

Solution :

Two polygons of the same number of sides are similar, if

(i) All the corresponding angles are equal and

(ii) Their corresponding sides are in the same ratio (or proportion).

In Quadrilaterals ABCD and PQRS

The corresponding angles do not appear equal

∠A ≠ ∠P; where ∠A = 90° and ∠P ≠ 90°

∠B ≠ ∠Q

Corresponding angles are not equal

Hence , first condition not satisfied. So they are not similar quadrilaterals .