M L Aggarwal Solutions for Exercise 1: EXERCISE 11

If $\mathrm{D}, \mathrm{E} \mathrm{and} \mathrm{F}$ are mid points of the sides $\mathrm{AB}, \mathrm{BC} \mathrm{and} \mathrm{CA}$ respectively of an isosceles triangle $\mathrm{ABC},$ prove that $△\mathrm{DEF}$ is also an isosceles triangle.

Show that the quadrilateral formed by joining the mid-points of the adjacent sides of a square is also a square.

In the quadrilateral given below, $AB\parallel DC$. $E$ and $F$ are mid-points of non-parallel sides $AD$ and $BC$ respectively. Calculate: $EF$ (in $\mathrm{cm}$), if $AB=6 \mathrm{cm}$ and $DC=4 \mathrm{cm}$.

In the quadrilateral given below, $AB\parallel DC$. $E$ and $F$ are mid-points of non-parallel sides $AD$ and $BC$ respectively. Calculate: $AB$ (in $\mathrm{cm}$), if $DC=8 \mathrm{cm}$ and $EF=9 \mathrm{cm}$.

In the adjoining figure,  $AD=BC. P, Q, R$and $S$ are mid-points of $AB, BD, CD$ and $AC$ respectively. Prove that $PQRS$ is a rhombus.

In the figure given below, $ABCD$ is a kite in which $BC=CD, AB=AD$. $E, F, G$ are mid-points of $CD, BC$ and $AB$ respectively. Prove that: $\mathrm{\angle }EFG=90°$.

In the figure given below, $ABCD$ is a kite in which $BC=CD, AB=AD$. $E, F, G$ are mid-points of $CD, BC$ and $AB$ respectively. Prove that the line drawn through $G$ and parallel to $FE$ bisects $DA$.

In the following figure, straight lines $l, m$ and $n$ are parallel to each other and $G$ is the mid-point of $CD$. Find $ED,$ if $FD=4.4 \mathrm{cm}$.