State the Mid-point Theorem.

State Basic Proportionality Theorem and its converse.

If the area of an equilateral triangle of side $a \mathrm{cm}$ is $\frac{\sqrt{k}}{m}{a}^2 {\mathrm{cm}}^2$ then find $k+m$.

If the altitude of two similar triangles are in the ratio $2:3,$ what is the ratio of their areas?

Each of the equal sides of an isosceles triangle is $25 \mathrm{cm}$. Find the length of its attitude if the base is $14 \mathrm{cm}$.

Find the length of each side of a rhombus whose diagonals are $24 \mathrm{cm}$ and $10 \mathrm{cm}$ long.