Bisectors of Angles of a Parallelogram Form a Rectangle

Q.

The diagonals of a rectangle PQRS intersects at O. If ∠QOR = 44°, ∠OPS =?

1. 82°

2. 68°

3. 75°

4. 52°

Q. Question 157
In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x.

Q. The two diagonals are equal in a

(a) parallelogram

(b) rhombus

(c) rectangle

(d) trapezium

Q.

The quadrilateral(PQRS) formed by the bisectors of the angles of a parallelogram(ABCD) is a square.

1. False

2. True

Q.

Use the following information to answer the next question.

In the given figure, PQRS is a parallelogram in which A and B are points on PQ and RS such that AP = AQ = SB = BR = 5 cm. The length of PC is 3 cm.

What is the length of the diagonal PR?

1. 9 cm

2. 10 cm

3. 11 cm

4. 13 cm

Q. Which of the following statement(s) is/are true , if a quadrilateral PQRS is formed by the angle bisectors of a parallelogram ABCD and PQ is not equal to QR?

1. Each interior angle of the quadrilateral PQRS is 60°.
2. PQRS is a rectangle.
3. PQRS is a square.
4. Each interior angle of the quadrilateral PQRS is 90°.

Q. In parallelogram ABCD, AR and DP are the angle bisectors of angles A and D respectively.If $\angle ADS=45°$, then the value of $\angle PSR$ is .

1. 90°
2. 45°
3. 135°
4. 75°

Q. What is the measure of each angle of the quadrilateral formed by the angle bisectors of a parallelogram?

1. 180°
2. 90°
3. 60°
4. 100°

Q. In parallelogram ABCD, AP, DP, BR and CR are the bisectors of their respective angles.If $\angle SPQ=90°$, then the value of $\angle ASB$ is .

1. 45°
2. 90°
3. 135°
4. 75°

Q.

The given figure shows parallelogram ABCD. Diagonals AC and BD of the parallelogram intersect at point O.

What is the perimeter of ΔABD?

1. 114 cm

2. 147 cm

3. 5x + 63 cm

4. 5x + 70 cm

Q. In the given figure, AP and BP are angle bisectors of $\angle$A and $\angle$B respectively which meet at point P of the parallelogram ABCD. Then $2\angle$APB$=$.

1. $\angle A+\angle C$
2. $\angle B+\angle D$
3. $\angle A+\angle B$
4. $2\angle C+3\angle B$

Q. In parallelogram ABCD, AR and DP are the angle bisectors of angles A and D respectively.If $\angle ADS=45°$, then the value of $\angle PSR$ is .

1. 90°
2. 45°
3. 135°
4. 75°

Q. If diagonals of rectangle ABCD bisects each other at point O, OA = 4 cm and OD = 3 cm, then the length of OB = and OC = .

1. 3 cm
2. 2 cm
3. 5 cm
4. 4 cm

Q. ABCD is a parallelogram, Burst the bubbles which represent the properties of parallelogram ABCD.

1. AB = CD
2. AB = BC
3. Angle A=Angle C
4. Angle C=Angle D
5. AC = BD
6. AB || CD
7. CD || DA
8. BC = AD
9. BC || AD
10. Angle B=Angle D

Q. The bisectors of the angles of a parallelogram enclose a:

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

Q. In the figure, $ABCD$ is a parallelogram whose diagonals intersect each other at $O$. A line segment $EOF$ is drawn to meet $AB$ at $E$ and $DC$ at $F$. Prove that $OE=OF$.

Q. ABCD is a parallelogram, Burst the bubbles which represent the properties of parallelogram ABCD.

1. AB = CD
2. AB = BC
3. Angle A=Angle C
4. Angle C=Angle D
5. AC = BD
6. AB || CD
7. CD || DA
8. BC = AD
9. BC || AD
10. Angle B=Angle D

Q. In parallelogram ABCD, AP, DP, BR and CR are the bisectors of their respective angles.If $\angle SPQ=90°$, then the value of $\angle ASB$ is .

1. 45°
2. 90°
3. 135°
4. 75°

Q. $\text{If one angle of parallelogram is}{90}^{\circ },\text{then all the other angles are equal to}$.

1. ${90}^{\circ }$
2. ${180}^{\circ }$
3. ${45}^{\circ }$

Q. In parallelogram ABCD, AR and DP are the angle bisectors of angles A and D respectively.If $\angle ADS=45°$, then the value of $\angle PSR$ is .

1. 90°
2. 45°
3. 135°
4. 75°