Parallelograms and their Properties

If quadrilateral $EFGH$ is a parallelogram, with diagonal $EG=12 \mathrm{cm}$, find the length of $EO$ (in $\mathrm{cm}$)?

Find the value of $x$ (in degrees) for the quadrilateral $ABCD$ to be a parallelogram? 

Find the value of $z$, for parallelogram $ABCD$

In a quadrilateral $ABCD$ , diagonal $AC$ and $BD$ bisect each other at point $O$ . The quadrilateral $ABCD$ is a _____

In a quadrilateral $MNOP$ , $MN\parallel OP$ and $NO\parallel MP$. The quadrilateral is a _____

Two adjacent angles of a parallelogram are $(2x+25)°$ and $(3x-5)°.$ The value of $x$ is

The opposite angles of a parallelogram are of equal measure.

If one of the angles of a parallelogram is $80°$, then the value of opposite angle is

In $\mathrm{\Delta }\mathrm{A}\mathrm{B}\mathrm{C}$ and $\mathrm{\Delta }\mathrm{D}\mathrm{E}\mathrm{F}, \mathrm{A}\mathrm{B}=\mathrm{D}\mathrm{E}, \mathrm{A}\mathrm{B}\parallel \mathrm{D}\mathrm{E}, \mathrm{B}\mathrm{C}=\mathrm{E}\mathrm{F}$ and $\mathrm{B}\mathrm{C}\parallel \mathrm{E}\mathrm{F}.$ Vertices $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are joined to vertices $\mathrm{D},\mathrm{}\mathrm{E}$ and $\mathrm{F}$ respectively. Then, the quadrilateral $\mathrm{A}\mathrm{B}\mathrm{E}\mathrm{D}$ is a parallelogram.
 

$ABCD$is a parallelogram in which $\angle ADC = 75°$ and side $AB$ is produced to point$E$ as shown in the figure. If $x + y=k°$ then find $k$.

The lengths of the diagonals of a rhombus are $24 \mathrm{cm}$ and $18 \mathrm{cm}$ respectively. If the length of each side of the rhombus is $k \mathrm{cm}$, find the value of $k$.

In a quadrilateral $PQRS$, opposite angles are equal. If $SR=2 \mathrm{cm}$, $PR=5 \mathrm{cm}$ and $PQ=k \mathrm{cm}$, then find the value of $k$. 

 In the adjoining figure, $ABCD$ is a parallelogram in which $\angle BAO=35°,\angle DAO=40°$ and $\angle COD=105°$. If $\angle CBD=y°$, find the value of $y$.

 In the adjoining figure, $ABCD$ is a parallelogram in which $\angle BAO=35°, \angle DAO=40°$ and $\angle COD=105°.$ If $\angle ODC=k^{\circ }$, then find the value of $k$.

Which of the following is true for a parallelogram?

Consider a parallelogram ABCD. Fill the blanks to find the type of parallelogram obtained if the diagonals of the parallelogram are equal.

In ∆ ABC and ∆ ABD,

AB is the common side.

AC = BD (Diagonals are equal)

AD = BC (Opposite sides of a parallelogram are equal)

∴ By SSS rule of congruency, the ∆ ABC and ∆ ABD are congruent.

∠ DAB = ∠ CBA (By CPCT)

Similarly,

∠ CDA = ∠ DCB

But ∠ DAB + ∠ CBA = 180 degrees (Co interior angles of parallel lines are supplementary)

∴ ABCD is a _____.

Jaya had a set of 6 identical matchsticks and was trying to make a parallelogram with them. If one matchstick represents one side of the parallelogram, then, with how many matchsticks could she make the parallelogram?

The diagonals of a quadrilateral bisect each other. Prove that this quadrilateral is parallelogram.

In a parallelogram, adjacent angles are equal.

In a _____ opposite sides are equal, opposite angles are equal and diagonals bisect one another (Parallelogram/Trapezium/Kite/Arrowhead).