Experimental Verification of Properties of Quadrilateral

If $(1, 2), (4, y), (x, 6)$ and $(3, 5)$ are the vertices of a parallelogram taken in order. Find $x$ and $y$.

$ABCD$ is a quadrilateral in which $\angle \mathrm{A}=2\mathrm{x}+1°,\angle \mathrm{B}=4\mathrm{x}-10°,\angle \mathrm{C}=\mathrm{x}+15°,\angle \mathrm{D}=\mathrm{x}+10°$ then $x$ is____

If the opposite angles of a quadrilateral are equal, then this will be a parallelogram.

The diagonals of a rectangle $ABCD$ intersect at point $O$. If $BD= 8 \mathrm{cm}$, $OC= ?$ State with reason.

Prove that "In a parallelogram, opposite sides are equal."

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

$\mathrm{ABCD}$ is a quadrilateral. In which angle $\mathrm{A}= x+1$, angle $\mathrm{B}= 3x+1$, angle $\mathrm{C}= 2x+1$, angle $\mathrm{D}= x+6$ . Find the value of $x$. (Correct the answer to two decimal places).

Find the values of $x,y,z. \text{Given} PQ\left|\right| SR \text{and} PS\left|\right|QR$

In the given figure, $ABCD$ is a rhombus where $AC=12 \mathrm{cm}, \mathrm{BD}=16 \mathrm{cm}$. Find the value of $AB$?

$\mathrm{ABCD}$ 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 $CD$.

Angles of a quadrilateral are $\left(2x+8\right)°,\left(x-11\right)°,50°\text{and} 100°$.What is the measure of the largest angle in the quadrilateral?

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 given kite $WEAR, \angle WEA=50°$. The sum of $\angle WEA$ and its opposite angle is $130°$. Find the measure of $\angle EWR$ and $\angle EAR$.

In the figure, $ABCD$ is a trapezium and $AD=AE$.

Find the value of $x$.

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

Find $\angle ADB$.

Find $\angle DAB$.

Find $x$.

Find $\angle ADB$

Find $\angle DAB$