Question : $D$ and $E$ are points of the sides $AB$ and $AC$, respectively of $\triangle ABC$ such that $DE$ is parallel to $BC$ and $AD:DB=7: 9$. If $CD$ and $BE$ intersect each other at $F$, then find the ratio of areas of $\triangle DEF$ and $\triangle CBF$.

Question : D, E, and F are the midpoints of the sides BC, CA, and AB, respectively of a $\triangle ABC$. Then the ratio of the areas of $\triangle DEF$ and $\triangle ABC$ is:

Question : In equilateral $\triangle $ABC, D and E are points on the sides AB and AC, respectively, such that AD = CE. BE and CD intersect at F. The measure (in degrees) of $\angle $CFB is:

Question : Diagonals of a trapezium $ABCD$ with $AB \parallel CD$ intersect each other at the point $O$. If $AB = 2CD$, then the ratio of the areas of $\triangle AOB$ and $\triangle COD$ is:

Question : In $\triangle$ABC and $\triangle$DEF, $\angle$A = $55^{\circ}$, AB = DE, AC = DF, $\angle$E = $85^{\circ}$ and $\angle$F = $40^{\circ}$. By which property are $\triangle$ABC and $\triangle$DEF congruent?