Ex 6.1 Class 10 Maths

Ex 6.1 

Class 10 

Maths

1. Fill in the blanks by 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)  similar

(ii) similar

(iii) equilateral

(iv)( a) equal (b) proportional

2.Give two different examples of pairs of

(i) similar figures.
(ii) non-similar figures.

Solution:

(i) (a) Two equilateral triangles of  3 cm and 3 cm.

(b) Two squares of sides 3 cm and 5 cm.

(ii)

(a) A quadrilateral and a rectangle.

(b) A triangle and a parallelogram.

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

Proof:

In Quadrilaterals  $ABCD$ and $PQRS$

$$\begin{array}{c}\frac{A\mathrm{B/}}{PQ}=\frac{B\mathrm{C/}}{QR}=\frac{C\mathrm{D/}}{RS}=\frac{D\mathrm{A/}}{SP}=\frac{\mathrm{3/}}{8}\end{array}$$

 Corresponding sides are in proportion

But $\angle A\ne \angle P;\angle B\ne \angle \mathrm{Q,}$

 Corresponding angles are not equal

$\square ABCD\nsim \square PQRS$

No, Quadrilateral $ABCD$ is not similar to Quadrilateral $PQRS$