Diagonals of Parallelogram Bisect Each Other

Q. In the given figure, ABCD is a quadrilateral and $\angle ADC=a^{\circ },\angle BCD=b^{\circ }.$ AO and BO are bisectors of $\angle DAB$ and $\angle ABC$ respectively meeting at O. Find $\angle AOB$ in terms of $a^{\circ }$ and $b^{\circ }$.

1. $a+b$
2. $\frac{(a+2b)}{2}$
3. $\frac{a+b}{2}$
4. $(a+2b)\times 2$

Q. In a parallelogram, the ___ bisect each other.

1. angles
2. diagonals
3. opposite sides
4. vertices

Q.

Which among the following has the most number of diagonals?

1. Triangle

2. Quadrilateral

3. Pentagon

4. Can't be determined

Q.

Which among the given statements is correct?

1. Only 2
2. Only 3
3. Both 2 & 3
4. All of them

Q. If ABCD is a parallelogram, then the angle bisectors of $\angle A$ and $\angle D$ meet at ‘O’. The measure of $\angle AOD$ is ${45}^{\circ }$​

1. 
2. 

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. ABCD is a parallelogram. The angle bisectors of $\angle Aand\angle D$ meet at O. Find the measure of $\angle AOD.$

1. ${120}^{\circ }$
2. ${35}^{\circ }$
3. ${40}^{\circ }$
4. ${90}^{\circ }$

Q.

ABCD is a rectangle. If OB = x + 2 and AC = 5x - 2, then find the measure of AC.

1. 6 units

2. 7 units

3. 9 units

4. 8 units

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 similar triangles

4. A parallelogram has 4 diagonals

Q.
Points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that AP = CQ. Which of the following is correct?

1. AC = CD
2. AC and PQ bisect each other.
3. AC = PQ
4. None of the above