# Properties of Parallelogram

## Trending Questions

**Q.**A quadrilateral is a parallelogram if a pair of its opposite sides are parallel and congruent.

- True
- False

**Q.**

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

True

False

**Q.**Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Which of the following is an angle of the parallelogram?

- 54°
- 72°
- 37°
- 25°

**Q.**

Prove that the opposite sides of a parallelogram are equal.

**Q.**

If one pair of opposite sides of a quadrilateral are equal and parallel, then the other pair will be:

Equal but not parallel

Parallel but not equal

Equal and parallel

Cannot be determined

**Q.**

$P,Q,R,\mathrm{and}S$ are respectively the mid-points of the sides $AB,BC,CD,\mathrm{and}DA$ of a quadrilateral $ABCD$ in which $AC=BD$. Prove that $PQRS$ is a rhombus.

**Q.**In a quadrilateral PQRS, PQ=RS and PQ∥RS, then what is quadrilateral PQRS?

- Parallelogram
- Square
- Rhombus
- Kite

**Q.**If each pair of opposite sides of a quadrilateral are equal, then it is a :

- Square
- Parallelogram
- Rhombus
- Kite

**Q.**In a parallelogram ABCD, ∠A=60∘, then-

- ∠B=60∘
- ∠C=60∘
- ∠D=120∘
- ∠B=120∘

**Q.**

Prove that if in a quadrilateral each pair of opposite Angles are equal then it is a parallelogram.

**Q.**

If any two adjacent angles in a quadrilateral are supplementary, then the quadrilateral is _________.

rectangle

square

trapezium

parallelogram

**Q.**The opposite sides of a quadrilateral are parallel. If one angle of the quadrilateral is 60°, find the other angles.

**Q.**

A quadrilateral with two pairs of parallel sides and four congruent sides is a………

Trapezium

kite

rhombus

rectangle

**Q.**

If any two adjacent angles in a quadrilateral are supplementary, then the quadrilateral is

Parallelogram

rectangle

square

Trapezium

**Q.**

ABCD is a parallelogram. P is a point on AD such that AP=13AD and Q is a point on BC such that CQ=13BC. Prove that AQCP is a parallelogram.

**Q.**

ABCD is a parallelogram in which P, Q, R and S are the mid points of sides AB, BC CD and DA respectively. Then,

PQ > RS

PQ = ½ CA

PQ < RS

PQ = RS

**Q.**(i) $\square $ABCD is a parallelogram. The ratio of $\angle $A and $\angle $B of this parallelogram is 5 : 4. Find the measure of $\angle $B.

**Q.**

In the adjoining figure, WXYZ is a parallelogram. The values of a and b is:

a = 15 and b = 4

a = 9 and b = 9

a = 12 and b = 8

a = 16 and b = 10

**Q.**

(i) The alternate angles formed by two parallel lines and their transversal are congruent.

**Q.**Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that arAOD = arBOC. Prove that ABCD is a trapezium.

**Q.**AB=CB, AB=CD and EF bisects BD at G. Prove that G is midpoint of EF

**Q.**One angle of a cyclic trapezium is triple the other. find the measure of the smaller angle

**Q.**In parallelogram ABCD of the accompanying diagram, line DP is drawn bisecting BC at N and meeting AB (extended) at P. From vertex C, line CQ is drawn bisecting side AD at M and meeting AB (extended) at Q. Lines DP and CQ meet at O. Find the ratio of area of triangle QPO and area of the parallelogram ABCD.

- 9 : 8
- 9 : 7
- 7 : 9
- 8 : 9

**Q.**The perimeter of the parallelogram ABCD is 24 cm with its two adjacent sides in the ratio 2:1. Find the length of these two adjacent side.

- 6 cm, 3 cm
- 4 cm, 2 cm
- 8 cm, 4 cm
- 10 cm, 5 cm

**Q.**The perimeter of a parallelogram is 170 cm. One of its sides is greater than the other by 15 cm. What is the length of the larger side of the parallelogram (in cm)?

- 50

**Q.**Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

**Q.**

Which of the following properties describe a trapezium?

A pair of opposite sides is parallel.

The diagonals bisect each other.

The diagonals are perpendicular to each other.

The diagonals are equal.

**Q.**In a parallelogram, opposite angles are ________ and adjacent angles are _________.

- equal, supplementary
- supplementary, equal
- complementary, supplementary
- equal, complementary

**Q.**Given below is a parallelogram. AC and BD are diagonals. If AO = x + y, OC = 5y, DO = 3x, OB = 12, then find x and y.

- x = 2, y = 3
- x = 1, y = 4
- x = 3, y = 2
- x = 4, y = 1

**Q.**ABCD is a rhombus. The length of AB is (2x+4) cm and the length of CD is (x+10) cm. The perimeter of the rhombus is

- 32 cm
- 16 cm
- 48 cm
- 64 cm