Parallelogram

Q. A trapezium can be a parallelogram but can a parallelogram be a trapezium?

Q.

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Q.

Difference between trapezium and trapezoid.

Q.

Square, rectangle and rhombus are all parallelograms.

1. True

2. False

Q.

If both pairs of opposite sides of a quadrilateral are parallel, then it is called:

1. All of these

2. Circle

3. Parallelogram

4. Triangle

Q.

Is a trapezium a parallelogram?

Q.

If all sides of a quadrilateral are equal, it is a __________.

Q.

Q.

The bisectors of any two adjacent angles of a parallelogram intersect at

1. ${45}^{\circ }$

2. ${60}^{\circ }$

3. ${30}^{\circ }$

4. ${90}^{\circ }$

Q. Question 6
Is the following statement true? Why?
''Two quadrilaterals are similar if their corresponding angles are equal”.

Q.

The figure formed by joining the midpoints of the adjacent sides of a quadrilateral is a

(a) rhombus

(b) square

(c) rectangle

(d) parallelogram

Q.

Prove that the line segment joining the mid-points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides. [4 MARKS]

Q.

In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of $\angle A$ meets DC in E. AE and BC produced meet at F. The length of CF is __ cm.

Q.

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Q. In the given figure, ABCD is a rhombus, then the value of 'x'is

1. ${45}^{\circ }$
2. ${50}^{\circ }$
3. ${30}^{\circ }$
4. ${65}^{\circ }$

Q.

$ABCD$ is a parallelogram and $AP$ and$CQ$ are perpendiculars from vertices $A$ and $C$ on diagonal $BD$.

Show that $\left(\mathrm{i}\right)\mathrm{\Delta APB}\cong \mathrm{\Delta CQD}$

$\left(\mathrm{ii}\right)\mathrm{AP}=\mathrm{CQ}$

Q.

In a ||gm ABCD, if $\angle A=(2x+25{)}^{\circ }$ and $\angle B=(3x-5{)}^{\circ }$, find the value of x and the measure of each angle of the parallelogram.

Q.

D, E and F are respectively the mid-points of the sides BC, CA and AB of a $△$ABC. Show that
(i) BDEF is a parallelogram.(ii) ar ($△$DEF) = $\frac{1}{4}$ ar ($△$ABC). [4 MARKS]

Q. If one angle of a parallelogram is twice of its adjacent angle, find the angles of the parallelogram.

Q.

The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a

1. rectangle

2. parallelogram

3. square

4. rhombus

Q.

Prove that by joining the midpoints of any quadrilateral, we get a parallelogram.

Q. A quadrilateral is a parallelogram, if

1. Opposite sides are equal.
2. Opposite angles are equal.
3. Diagonals bisect each other.
4. A pair of opposite sides are equal and parallel.

Q.

In the adjoining figure, ABCD is a parallelogram in which $\angle DAB={80}^{\circ }and\angle DBC={60}^{\circ }$. Calculate $\angle CDBand\angle ADB$.

Q.

Which of the following is not true for a Parallelogram?

1. opposite sides are equal

2. opposite angles are equal

3. opposite angles are bisected by the diagonals

4. diagonals bisect each other.

Q.

P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Then:

1. DA = AR and CQ = QR

2. PA = AR

3. CR = DR

4. CR = 2CQ

Q.

If every pair of adjacent sides of a quadrilateral are equal, then the quadrilateral is a

1. Square only

2. Rectangle or a trapezium

3. Square or a Rhombus

4. Rhombus only

Q.

Which of the following is not a necessary condition for a quadrilateral $ABCD$ to be a parallelogram:

1. $AB\parallel CD$

2. $\angle A={50}^{\circ },\angle C={50}^{\circ },\angle B={130}^{\circ }$

3. $AB\perp AD$

4. $AB=CD$

Q.

Choose the correct statement

1. Every parallelogram is a trapezium

2. Every parallelogram is a rectangle

3. Every parallelogram is a rhombus

4. Every rectangle is a square

Q.

Square, rectangle and rhombus are all parallelograms.

1. True

2. False

Q.

Find the measure of each angle of a parallelogram, if one of its angles is ${30}^{\circ }$ less than twice the smallest angle.