Exercise 6.1

(i) All circles are similar.
(ii) All squares are similar.
(iii) All equilateral triangles are similar.
(iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are equal and (b) their corresponding sides are proportional.

Give two different examples of pair of (i) similar figures. (ii) non-similar figures.

State whether the following quadrilaterals are similar or not:

(i) Quadrilateral $ABCD$ with $AB = 2\text{ cm},\; BC = 3\text{ cm},\; CD = 2\text{ cm},\; DA = 3\text{ cm}$ and quadrilateral $EFGH$ with $EF = 4\text{ cm},\; FG = 6\text{ cm},\; GH = 4\text{ cm},\; HE = 6\text{ cm}$.

(ii) Quadrilateral $ABCD$ with $AB = 2\text{ cm},\; BC = 3\text{ cm},\; CD = 4\text{ cm},\; DA = 5\text{ cm}$ and quadrilateral $EFGH$ with $EF = 4\text{ cm},\; FG = 6\text{ cm},\; GH = 8\text{ cm},\; HE = 10\text{ cm}$.

(iii) Quadrilateral $ABCD$ with $AB = 2\text{ cm},\; BC = 2\text{ cm},\; CD = 2\text{ cm},\; DA = 2\text{ cm}$ and quadrilateral $EFGH$ with $EF = 3\text{ cm},\; FG = 3\text{ cm},\; GH = 3\text{ cm},\; HE = 3\text{ cm}$.

(iv) Quadrilateral $ABCD$ with $AB = 2\text{ cm},\; BC = 3\text{ cm},\; CD = 4\text{ cm},\; DA = 5\text{ cm}$ and quadrilateral $EFGH$ with $EF = 3\text{ cm},\; FG = 4\text{ cm},\; GH = 5\text{ cm},\; HE = 6\text{ cm}$.