For the correspondence $ABC \leftrightarrow RPQ$ between $\Delta ABC$ and $\Delta PQR$,$\angle B$ corresponds to $\ldots \ldots \ldots \ldots$

$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid-point of $BC$. The ratio of the areas of triangles $ABC$ and $BDE$ is

Fill in the blanks 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)

Give two different examples of pairs of non-similar figures.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

Give two different examples of pairs of similar figures.