Deducing Properties of Parallelogram

Q.

Prove that the diagonals of an isosceles trapezium are equal.

Q.

Prove that the midpoints of the adjacent sides of a rectangle will form a rhombus. [4 MARKS]

Q.

Find the measure of all the angles of a parallelogram, if one angle is ${12}^{\circ }$ more than twice the smallest angle. [3 MARKS]

Q.

Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Q.

In the given figure, AC = CE and AB || ED. The value of x is :

1. 12
2. 15
3. 18
4. 20

Q.

Prove logically the diagonals of a parallelogram bisect each other. Show conversely that a quadrilateral in which diagonals bisect each other is a parallelogram.

Q.

In the parallelogram ABCD, $\Delta AOB$ is congruent to

1. $\Delta ABC$

2. $\Delta AOC$

3. $\Delta AOB$

4. $\Delta COD$

Q.

Squares ABPQ and ADRS are drawn on the sides AB and AD of a parallelogram ABCD. Which of the following options is correct?

1. None of these

2. $\angle SRD=\angle ADC$

3. $\angle SAQ=\angle ABC$

4. $\angle SAD=\angle ABC$

Q.

Find the measure of ∠P and ∠S, if in the following figure. (If you find m∠R, is there more than one method to find m∠P?)

Q. Find the value of $y$ if $ABCD$ is a parallelogram.

1. 7
2. 5
3. 6
4. 2

Q.

In the following figure, if BO = 10 cm, then the length of the diagonal BD is

1. 14 cm

2. 24 cm

3. 16 cm

4. 20 cm

Q.

In the given figure, ABCD is a parallelogram. E is a point on DC. If AE bisects $\angle$A and BE bisects $\angle$B, then which of the following statements is correct?

1. AB = BC

2. AB = 2 BC

3. AB = 12BC

4. AB = 3 B

Q.

Discuss the important properties of parallelogram with appropriate diagrams.

Q. ABCD is a parallelogram with AC and BD as diagonals, intersecting each other at O.


If AC = 12 cm, then AO = ____ cm.

1. 6

Q.

In the following figure, if AO = 4 cm, then the length of the diagonal AC is _____.

1. 6 cm

2. 12 cm

3. 8 cm

4. 16 cm

Q. If the diagonals of a parallellogram HOPE bisect at A, then $△HOA\cong$ and $△OPA\cong$
.

1. $△PEA$
2. $△HEO$
3. $△EHA$
4. $△PEA$

Q. If KITE is a parallelogram, then which angle is equivalent to the sum of $\angle A$ and $\angle R$ ?

1. 
2. 
3. 
4. 

Q.

The adjacent angles of a parallelogram are___.

Q.

If BDEF and FDCE are parallelograms, then "D" lies equidistant to points B and C.

1. True

2. False

Q.

Find $\angle ABD$ in the parallelogram ABCD.

1. ${25}^{\circ }$

2. ${30}^{\circ }$

3. ${75}^{\circ }$

4. ${45}^{\circ }$

Q.

In the given figure, if ACFD and ABED are parallelograms, then which of the following statements are true?

1. AC = DF

2. BC = EF

3. AB = DE

4. All the above

Q. Prove that the diagonals of a rhombus bisect each other at right angles.

Q.

The adjacent angles of a parallelogram are___.

Q. In the adjacent figure, ABCD is a parallelogram and line segments AE and CF bisect the angles A and C respectively. Show that AE||CF.

Q.

Consider the figure and choose the correct option.

1. ΔABC ≅ ΔDEF

2. ΔABC ≅ ΔFED

3. ΔABC is not congruent to ΔFED

4. ΔABC ≅ ΔDFE

Q.

In any parallelogram, the diagonals

1. cut each other in the ratio 1:2

2. cut each other in the ratio 3:1

3. cut each other in the ratio 3:4

4. bisect each other

Q. Choose the correct options:

1. Diagonals in a parallelogram are equal.
2. Diagonals in a parallelogram bisect each other.
3. A diagonal in a parallelogram divides it into two congruent triangles.
4. A parallelogram has 4 diagonals.

Q.

In the parallelogram ABCD, $\Delta AOB$ is congruent to

1. $\Delta ABC$

2. $\Delta AOC$

3. $\Delta AOB$

4. $\Delta COD$

Q.

In the parallelogram ABCD, find x.​

1. ${60}^{\circ }$

2. ${50}^{\circ }$

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

4. ${40}^{\circ }$