Q3 of 95 Page 6

Give two examples of:

(i) Congruent figures.


(ii) Similar figures which are not congruent.


(iii) Non-similar figures.

(i) (a) Two circles having radii 2cm and different centres



In this, both of them have the same radii, but their centres are different.


(b) Two squares having the same length of side 5cm



We know that in a square all the sides are equal and all angles are of 90°. So, these two squares are congruent.


(ii) (a) Two equilateral triangles having sides 1cm and 2cm.



In case of equilateral triangles, all the sides are equal, and all the angles are of 60°.


But here, their corresponding angles are equal, but sides of triangle ABC and PQR are not equal in length.


So, they are similar figures but not congruent.


(b) Two circles having radii 1cm and 2cm



Both of the figures are of circle but they are having different radii. So, they are similar but not congruent.


(iii) (a) A rhombus and a rectangle


In the case of a rhombus, all the sides are equal, and the angles can either be right angles or combination of acute and obtuse angles but in rectangle all angles are equal, and opposite sides are equal.


Hence, a rhombus and a rectangle are non-similar figures.


(b)


Here, both of the triangles are right-angled but other two angles are not equal. So, these are not similar figures.


More from this chapter

All 95 →
1

Fill in the blanks with the correct word given in brackets:

(i) All squares are having the same length of sides are……….


[similar, congruent, both congruent and similar]


(ii) All circles having the same radius are ……….


[similar, congruent, both congruent and similar]


(iii) All rhombuses having one angle 90o ………. [similar, congruent]


(iv) All photographs of a given building made by the same negative are ………..


[similar, congruent, both congruent and similar]


(v) Two polygons having equal numbers of sides are similar if their corresponding angles are equal and their corresponding sides are ……….


[equal, proportional]

 2

State which of the following statements are true and which are false:

(i) Two similar figures are congruent.


(ii) All congruent figures are similar.


(iii) All isosceles triangles are similar.


(iv) All right-angled triangles are similar.


(v) All squares are similar.


(vi) All rectangles are similar.


(vii) Two photographs of a person made by the same negative are similar.


(viii) Two photographs of a person one at the age of 5 years and other at the age of 50 years are similar.

 4

State whether the following right-angled triangles are similar or not:

 5

State whether the following rectangles are similar or not.