Important Results Related to Parallelograms

Q.

In a parallelogram, if a diagonal bisects the angles through which it passes, then the parallelogram is a ___

1. Square

2. Rhombus

3. Rectangle

4. Trapezium

Q.

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

1. 
2. 
3. 
4. 

Q.

A quadrilateral with each angle ${90}^{\circ }$ is called a square.

1. False

2. True

Q.

The angle-bisectors of a parallelogram form a quadrilateral as shown in the figure. Then ABCD is a _____.

1. It's a parallelogram with three acute angles

2. It's a parallelogram with three obtuse angles

3. It's a parallelogram with each angle equal to

4. It's a parallelogram with adjacent sides equal

Q.

If the rhombus has a perimeter of 28 cm then the length of its side is:

1. 14 cm

2. 7 cm

3. 21 cm

4. 10 cm

Q.

Two adjacent angles of rhombus are $(3x-40{)}^{\circ }and(2x+20{)}^{\circ }.$ The measurement of the greater angle is

1. 
2. 
3. 
4. 

Q. The following figure is a rhombus. Find the values of the unknowns x, y and z.

1. $x={90}^{\circ },y={60}^{\circ }andz={60}^{\circ }$
2. $x={90}^{\circ },y={90}^{\circ }andz={90}^{\circ }$
3. $x={30}^{\circ },y={60}^{\circ }andz={60}^{\circ }$
4. $x={90}^{\circ },y={30}^{\circ }andz={30}^{\circ }$

Q. Question 4
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measures.

Q.

Which of the following are true?

i) All squares are rhombuses.

ii) All parallelograms are rectangles.

iii) All rhombuses are trapeziums

iv) All squares are rectangles.

1. ii, iii

2. i, ii

3. i, iii, iv

4. None of these

Q. Question 1 (i)
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD = ..........

Q. $\text{Two adjacent angles of rhombus are}3x-{40}^{\circ }\text{and}2x+{20}^{\circ }.\text{Find the}\text{measurement of the greater angle.}$

1. ${160}^{\circ }$
2. ${100}^{\circ }$
3. ${80}^{\circ }$
4. ${120}^{\circ }$

Q. If the base and height of a parallelogram are 14 cm and 7 cm respectively, find its area.

1. 49 sq. cm
2. 98 sq. cm
3. 63 sq. cm
4. 84 sq. cm

Q. Parallelograms on the same base and having equal areas lie between the same parallels.

1. False
2. True

Q.

In square PQRS if $PQ=3x-7$ and $QR=x+3$, Find PS

1. 8

2. 10

3. 6

4. 12

Q.

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O . If $\angle DAC={35}^{\circ }and\angle AOB={80}^{\circ }$, then $\angle DBC$ is equal to ___.

1. ${55}^{\circ }$

2. ${45}^{\circ }$

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

4. ${35}^{\circ }$

Q. Two adjacent angles of a parallelogram are $(3x-4{)}^{\circ }$ and $(3x+10{)}^{\circ }$. Find the angles of the parallelogram.

1. $\angle A={83}^{\circ },\angle B={97}^{\circ },\angle C={83}^{\circ },\angle D={97}^{\circ }$
2. $\angle A={83}^{\circ },\angle B={83}^{\circ },\angle C={97}^{\circ },\angle D={97}^{\circ }$
3. $\angle A={97}^{\circ },\angle B={83}^{\circ },\angle C={97}^{\circ },\angle D={83}^{\circ }$
4. $\angle A={78}^{\circ },\angle B={89}^{\circ },\angle C={78}^{\circ },\angle D={89}^{\circ }$

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.

A rectangle can be thought of as a special parallelogram.

Q.

The given figure is a rectangle in which $x:y=3:7$

Find angle $xandy.$

1. $x={27}^{\circ }$

   $y={63}^{\circ }$

2. $x={63}^{\circ }$

   $y={27}^{\circ }$

3. $x={21}^{\circ }$

   $y={69}^{\circ }$

4. $x={65}^{\circ }$

   $y={23}^{\circ }$

Q. Measures of opposite angles of a parallelogram are (3x − 2)$°$ and (50 − x)$°$. Find the measure of its each angle.

Q. $\text{The diagonals AC and BD of a}\text{parallelogram ABCD intersect each other}\text{at the point O . If}\angle DAC={35}^{\circ }\text{and}\angle AOB={80}^{\circ },\text{then find the value of}\angle DBC.$

1. ${45}^{\circ }$
2. ${55}^{\circ }$
3. ${75}^{\circ }$
4. ${35}^{\circ }$

Q.

Diagonals of quadrilateral ABCD bisect each other and $\angle B={75}^{\circ }$ , then the value of $\angle A$ is

1. 
2. 
3. 
4. 

Q.

With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can be said about lines AE and CF?

1. Can be parallel or perpendicular

2. Neither parallel nor perpendicular

3. Always perpendicular

4. Always parallel

Q.

In a rhombus PQRS, ∠SQR = 40° and PQ = 3 cm. Find ∠SPQ, ∠QSR and the perimeter of the rhombus.

Q.

To determine all angles of a parallelogram, which of the following is the minimum necessary condition?

1. Two angles are known.

2. Three angles are known.

3. Only one angle is known.

4. Length of sides should be known

Q.

The bisectors of any two adjacent angles of a parallelogram intersect at an angle of ___.

1. 
2. 
3. 
4. 

Q. two adjacent angles of a parallelogram have equal measure of each of the angles of the parallelogram. find the adjacent angles?

Q. Question 135
In a rectangle ABCD, AB = 25 cm and BC = 15 cm. In what ratio, does the bisector of $\angle C$ divide AB?

Q. O is any point inside a rectangle ABCD, then ${OB}^2+{OD}^2={OA}^2+{OC}^2$

1. true
2. false

Q. In square PORS:

$\text{If}PQ=3x–7\text{and}QR=x+3;\text{find PS}$