Q. 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.

Answer :

(i) This statement is false because all the congruent figures are similar, but similar figures need not be congruent.


E.g. 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.


(ii) This statement is true because all congruent figures are similar, but similar figures need not be congruent.


(iii) This statement is false because for two triangles to be similar to the angles in one triangle must have the same values as the angles in the other triangle. The sides must be proportionate.


E.g.



These are the two isosceles triangles having two equal sides, but we can see that the sides are not proportionate.


(iv) This statement is false.


Suppose these are two right-angled triangles



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


(v) This statement is true because all the angles in a square are right angles and all the sides are equal. Hence, a smaller square can be enlarged to the size of a larger square, and vice-versa is also true.


(vi) This statement is false because similarity preserves the ratio of length. Therefore, two rectangles with a different ratio between their sides cannot be similar.


(vii) This statement is true because photographs are produced by projecting the image from a negative through an enlarger to a photographic paper. The enlarger reproduces the image from the negative but makes it bigger. The images are not identical and are not of the same size, but they are similar.



(viii) This statement is false because here the photograph of a person is taken at the different ages.


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