Properties of Parallelogram

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

1. True
2. False

Q.

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

1. True

2. False

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

1. 54°
2. 72°
3. 37°
4. 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:

1. Equal but not parallel

2. Parallel but not equal

3. Equal and parallel

4. 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 $PQ\parallel RS$, then what is quadrilateral $PQRS$?

1. Parallelogram
2. Square
3. Rhombus
4. Kite

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

1. Square
2. Parallelogram
3. Rhombus
4. Kite

Q. In a parallelogram $ABCD$, $\angle$$A$=${60}^{\circ }$, then-

1. $\angle$$B$=${60}^{\circ }$
2. $\angle$$C$=${60}^{\circ }$
3. $\angle$$D$=${120}^{\circ }$
4. $\angle$$B$=${120}^{\circ }$

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 _________.

1. rectangle

2. square

3. trapezium

4. 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………

1. Trapezium

2. kite

3. rhombus

4. rectangle

Q.

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

1. Parallelogram

2. rectangle

3. square

4. Trapezium

Q.

$ABCD$ is a parallelogram. $P$ is a point on $AD$ such that $AP=\frac{1}{3}AD$ and Q is a point on $BC$ such that $CQ=\frac{1}{3}BC$. 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,

1. PQ > RS

2. PQ = ½ CA

3. PQ < RS

4. 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:

1. a = 15 and b = 4

2. a = 9 and b = 9

3. a = 12 and b = 8

4. a = 16 and b = 10

Q.

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.

1. 9 : 8
2. 9 : 7
3. 7 : 9
4. 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.

1. 6 cm, 3 cm
2. 4 cm, 2 cm
3. 8 cm, 4 cm
4. 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)?

1. 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?

1. A pair of opposite sides is parallel.

2. The diagonals bisect each other.

3. The diagonals are perpendicular to each other.

4. The diagonals are equal.

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

1. equal, supplementary
2. supplementary, equal
3. complementary, supplementary
4. 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.

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

1. $32cm$
2. $16cm$
3. $48cm$
4. $64cm$