Brijesh Dwevedi and Jitendra Gupta Solutions for Chapter: Quadrilaterals, Exercise 3: Exercise 8.3

$D$ and $E$ are the mid-points of sides $AB$ and $AC$, respectively of $∆ABC$. If the perimeter of $∆ABC=38 \mathrm{cm}$. Find the perimeter of $∆ADE$.

$D, E$ and $F$ are the mid-points of sides $BC, CA$ and $AB$, respectively of $∆ABC$. If perimeter of $∆ABC$ is $12.8 \mathrm{cm}$, then find the perimeter of $∆DEF$.

In the given figure, it is given that $BDEF$ and $FDCE$ are parallelograms. If $BD=8 \mathrm{cm}$, then determine $CD$.

In $∆ABC, AB=13 \mathrm{cm}, BC=16 \mathrm{cm}$ and $AC=8 \mathrm{cm}$. Find the perimeter of the triangle formed by joining the mid-points of the sides of the triangle.

$P, Q, R$ and $S$ are mid-points of the sides $AB, BC, CD$ and $DA$ respectively of a quadrilateral $ABCD$ in which $AC\perp BD.$ Prove that $PQRS$ is a rectangle.

$\mathrm{P},\mathrm{Q},\mathrm{}\mathrm{R}$ and $\mathrm{S}$ are the mid points of the sides $\mathrm{A}\mathrm{B},\mathrm{}\mathrm{B}\mathrm{C},\mathrm{}\mathrm{C}\mathrm{D}$ and $\mathrm{D}\mathrm{A}$ respectively of a quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ in which $\mathrm{A}\mathrm{C}=\mathrm{B}\mathrm{D}$. Prove that $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ is a rhombus.

In $∆ABC, AD$ is the median and $DE$ is parallel to $BA$, where $E$ is a point in $AC$. Prove that $BE$ is also a median.

In a $∆ABC$, median $AD$ is produced to $Y$ such that $AD=DY$. Prove that $ABYC$ is a parallelogram.