Properties of a Parallelogram

In a parallelogram $ABCD$, if $\angle A= 75°$ then $\angle C$ is equal to:

$PQRS$ is a  parallelogram. $PS$ is extended to $E$ such that $SR=SE$. $ER$ is extended to meet $PQ \text{at} F$. Prove $QF= QR$.

$\mathrm{XYZT}$ is a parallelogram. $\mathrm{E}$ and $\mathrm{F}$ are mid-points of sides $\mathrm{XY}$ and $\mathrm{ZT}$ respectively. $\mathrm{PQ}$ is any straight line that meets $\mathrm{XT}, \mathrm{EF}$ and $\mathrm{YZ}$ in points $\mathrm{P}, \mathrm{O}$ and $\mathrm{Q}$ respectively. Prove that $\mathrm{PO}=\mathrm{OQ}$.

$\mathrm{ABCD}$ is a parallelogram and $\angle DAB=60°$ . If the bisectors $AP\text{ and} BP$ of the angles $A \text{and} B$ respectively meet at $P$ on $CD$.

Prove that $P$ is the mid-point of $CD$.

In a parallelogram $PQRS$, diagonals$PR$ and $QS$ intersect each other at  $O$. If angle $SPR=24°$and angle $\mathrm{POQ}=60°,$. then what is the measure of angle $SQR$?

In the figure, $ABCD$ is a rhombus and $ABDE$ is a parallelogram.

Given that $EDC$ is a straight line and $\angle AED=36°$, find $\angle BAD$.

The diagonals of a square with area $9 {\mathrm{m}}^2$ divide the square into four non-overlapping triangles. What is the sum of the perimeter of the four triangles.

In the given figure, $ABCD$ is a parallelogram whose diagonals intersect each other at $O$. Through $O,PQ$ is drawn then prove that $OP=OQ$.

If $△PQR$ and $△LMN$ be two triangles given in such a way that $PQ\parallel LM, PQ=LM$ and $QR=MN$ and $QR\parallel MN$, then show that $PR\parallel LN$ and $PR=LN$.

In a parallelogram $PQRS$, T is the midpoint of $PQ$ and $ST$ bisects $\angle S$. Prove that: $\angle STR=90°$.

In a parallelogram $PQRS$, T is the midpoint of $PQ$ and $ST$ bisects $\angle S$. Prove that: $RT$ bisects$\angle R$.

In a parallelogram $PQRS$, T is the midpoint of $PQ$ and $ST$ bisects $\angle S$. Prove that: $QR=QT$.

If $A(-2, -1), B(a, 0), C(4, b)$ and $D(1, 2)$ are the vertices of a parallelogram $ABCD$, then find the values of $a$ and $b$.

If the length of parallel sides of a parallelogram is $\mathrm{m}$ and $\mathrm{n}$, each, then the perimeter is equal to:

Parallelograms on the same base and between the same parallel sides are:

The interior opposite angles of a parallelogram are:

Why every parallelogram is not a trapezium.

Every trapezium.is a parallelogram.

Every parallelogram is a trapezium.

If the base of parallelogram is $10 \mathrm{cm}$ and its corresponding height is $5 \mathrm{cm}$, then the area of parallelogram is: