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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)
To do:
We have to fill in the blanks.
Solution:
(i) All circles are similar.
All circles are of the same shape. They only differ in the size. Any circle can be scaled to form any other circle. Therefore, all circles are similar.
(ii) All squares are similar.
All squares are similar. Their size may not be equal but their ratios of corresponding parts will always be equal. As, the ratio of their corresponding sides is equal hence, the two squares are similar.
(iii) All equilateral triangles are similar.
All regular polygons with the same number of sides are similar to each other.
An equilateral triangle is a regular polygon with three sides. So, all equilateral triangles are similar.
(iv) Two polygons of the same number of sides are similar if their corresponding angles are (a) equal and their corresponding sides are (b) proportional.
A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
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