Diagonals of a Parallelogram

Q.

All rhombuses are parallelograms but all parallelograms are not rhombuses.

1. True

2. False

Q.

$\text{If the diagonals of a parallelogram are of equal lengths, the parallelogram is arectangle. Prove it.}$

Q. ABCD is a parallelogram in which $\angle DAO={40}^{\circ }$, $\angle BAO={35}^{\circ }and\angle COD={65}^{\circ }$ . Find $\angle ODC$.

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${80}^{\circ }$
4. ${90}^{\circ }$

Q. ABCD is a parallelogram. The angle bisectors of $\angle Aand\angle D$ meet at O. Find the measure of $\angle AOD.$

1. ${120}^{\circ }$
2. ${35}^{\circ }$
3. ${40}^{\circ }$
4. ${90}^{\circ }$

Q.

$\text{ABCD is a parallelogram. What kind of quadrilateral is it if :}\left(i\right)AC=BD\text{and AC is perpendicular to BD ?}\left(ii\right)\text{AC is perpendicular to BD but is not equal to it ?}\left(iii\right)AC=BD\text{but AC is not perpendicular to BD ?}$

Q.

Diagonals of a parallelogram ABCD intersect at O. AL and CM are drawn perpendiculars to BD such that L and M neon BD. Is AL = CM ? Why or why not ?

Q.

$\text{PQRS is a parallelogram whose diagonals intersect at M.}if\angle PMS={54}^{\circ },\angle QSR={25}^{\circ }and\angle SQR={30}^{\circ };find:\left(i\right)\angle RPS\left(ii\right)\angle PRS\left(iii\right)\angle PSR.$

Q.

$\text{In the given figure,}AB||EC,AB=ACandAEbisects\angle \text{DAC.Prove that:}$

$\left(i\right)\angle EAC=\angle ACB\left(ii\right)\text{ABCE is a parallelogram.}$

Q.

$\text{Given : Parallelogram ABCD in which diagonals AC and BD intersect at M.}\text{Prove : M is mid-point of LN.}$

Q. Question 9
In the figure, both RISK and CLUE are parallelograms. Find the value of x.

Q.

Points E and F lie on diagonal AC of a parallelogram ABCD such that AE = CF. What type of quadrilateral is BFDE ?

Q. ABCD is a parallelogram with AC and BD as diagonals, intersecting each other at O. If AO = 2 cm and BO = 3cm, then

1. AC + BD = 8 cm
2. AC + BD = 10 cm
3. AC + BD = 12 cm

Q.

The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why pot ?

Q.

The diagonal of a parallelogram divides it into two congruent triangles.

1. False

2. True

Q.

In the given figure, ABCP is a parallelogram and P is the mid point of CD. Then find which of the following option is correct?

1. $AP=\frac{1}{2}BC$

2. $PD=AP$

3. $OA=\frac{1}{2}CD$

4. $OB=\frac{1}{2}BD$

Q.

Question 4 (i)
Name the quadrilateral whose diagonals:

(i) Bisect each other.

Q. In parallelogram ABCD, if the bisector of adjacent angles A and D intersect each other at point P, then the value of $\angle APD={60}^{\circ }$. State with true or false.

1. True
2. False

Q.

$\text{The given figure shows parallelogram ABCD.}\text{Points M and N lie in diagonal BD such that}DM=BN.$

$\text{Prove that :}\left(i\right)\Delta DMC=\Delta BNAandsoCM=AN\left(ii\right)\Delta AMD\cong \Delta CNBandsoAM=CN\left(iii\right)\text{ANCM is a parallelogram.}$

Q. The following figures GUNS and RUNS are parallelograms. Find $x$ and $y$. (Lengths are in cm)

Q. Question 81
Fill in the blanks to make the statements true.
If the diagonals of a quadrilateral bisect each other, it is a ___.

Q. Question 160
Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x, if JF = 8x + 4 and EG = 24x - 8.

Q.

$\text{Prove that the diagonals of a paral lelogram bisect each other.}$

Q.

Identify all the quadrilaterals that have

(a) four sides of equal length

(b) four right angles

Q. Prove that the diagonals of a parallelogram bisect each other.

Q. Which of the following is not always true for a parallelogram?

1. Opposite sides are equal.
2. Opposite angles are bisected by the diagonals.
3. Opposite angles are equal.
4. Diagonals bisect each other.

Q. ABCD is a parallelogram whose area is 54 sq. cm. The area of triangle AEB is __ sq. cm.

1. 18
2. 13.5
3. 27
4. 6.75

Q. From the adjoining figure:
$DL\perp AB;BM\perp AD.$
$AB=12$ cm, $AD=5$ cm, $BM=8$ cm. Find $DL$

Q. The diagonals of a parallelogram divides it into ___ congruent triangles.

1. one
2. two
3. three
4. four

Q.

The diagonal of a parallelogram divides it into two congruent triangles.

1. True

2. False

Q.

5. Write the names of the following polygon.