Question

Fill in the blank using the correct word given in the brackets
(i) All circles are __________.(congruent, similar)
(ii) All squares are _________. (congruent,similar)
(iii) All __________ triangles are similar. (isosceles,equilateral)
(iv) Two polygon of the same number of sides are similar if
      (a) Their corresponding angles are ___________(equal,proportional)
      (b) Their corresponding sides are _____________(equal, proportional)

Answer 1

Hints: For number (i),(ii) keep in mind that two figures are congruent if they have the same shape and size but for similarity size doesn't matter. For (iii) one must remember that isosceles triangles have 2 equal sides regardless of which one but equilateral triangles have all sides equal. For (iv) in similarity angles must be equal and sides must be proportional.

Complete step by step solution:
(i) Circles may have different radii and that's the only parameter that matters to draw a circle so the shape of the circle will remain the same but the sizes may differ.
Therefore All Circles are similar is the correct statement.
(ii) Square has only one parameter and that is the length of any one of its sides because the rest remains the same. So, again the lengths of the sides may differ but the shape remains the same. Therefore, All squares are similar is the correct statement.
(iii) Have a look at the diagram below. On the left hand side there are two equilateral triangles; it can be easily observed that the sizes are different but the shape remains the same. But on the right hand side there are two isosceles triangles where the shape and size both are different therefore it cannot be a similar triangle. Which means all isosceles triangles are not similar. Therefore, all equilateral triangles are similar is the correct statement.

(iv) Keeping in mind that the size doesn't matter for similarity it can be easily told that the lengths of the sides maynot be equal but they have to be proportional and for shape angles plays a vital role regardless of lengths of the sides, so angles has to be equal
Therefore the correct statements are
(a) Their Corresponding angles are proportional.
(b) Their corresponding sides are equal.

Note: Always keep in mind that all congruent figures are similar but all similar figures are not congruent; Also angles be the key factor when we decide similarity and sides and angles both be the key factor when we decide congruence.