R. D. Sharma Solutions for Chapter: Quadrilaterals, Exercise 3: EXERCISE

In a parallelogram $\mathrm{ABCD}$, If the sum of angles $\angle \mathrm{C}$ and $\angle \mathrm{D}$ is $k°$, then find the value of $k$.

$ABCD$ is a square. $AC$ and $BD$ intersect at $O.$ If the measure of $\angle AOB$ is $k°$ , then find the value of $k$.

$ABCD$ is a rectangle with $\angle ABD=40°.$ If $\angle DBC=k°$, then find the value of $k$.

The sides $AB$ and $CD$ of a parallelogram $ABCD$ are bisected at $E$ and $F$. Prove that $EBFD$ is a parallelogram.

$P$ and $Q$ are the points of trisection of the diagonal $BD$ of a parallelogram $ABCD$. Prove that $CQ$ is parallel to $AP$. Prove also that $AC$ bisects $PQ$.

$ABCD$ is a square. $E,F,G$ and $H$ are points on $AB, BC, CD$ and $DA$ respectively, such that $AE=BF=CG=DH$. Prove that $EFGH$ is a square.

$ABCD$ is a rhombus, $EABF$ is a straight line such that  $EA=AB=BF$. Prove that $ED$ and $FC$ when produced meet at right angles.

$ABCD$ is a parallelogram, $AD$ is produced to $E$ so that  $DE=DC$ and $EC$ produced meets $AB$ produced in $F$. Prove that $BF=BC.$