Diagonals of a Parallelogram Bisect Each Other

Q.

Prove that the midpoints of the adjacent sides of a rhombus will form a rectangle.

Q.

AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD. Choose the correct option

1. AN = CP

2. AN ≠ CP

3. AN < CP

4. AN > CP

Q.

Find the length of the diagonal AC of the parallelogram ABCD when AE = 4x + 5 and EC = 3x + 7

1. 52 cm

2. 26 cm

3. 13 cm

4. Can not be determined

Q.

Assertion : In $\Delta ABC$, median AD is produced to X such that AD = DX. Then, ABXC is a parallelogram.
Reason : Diagonals AX and BC bisect each other at right angles.
Which of the following is correct?

1. If both assertion and reason are true and reason is the correct explanation of assertion
2. If both assertion and reason are true but reason is not the correct explanation of assertion
3. If assertion is true but reason is false
4. If assertion is false but reason is true

Q. P and Q are the mid-points of the opposite sides AB and CD of parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

Q.

In parallelogram RSTV, diagonals RT and VS intersect at Q. If RQ=5x+1 and QT =3x +15 find QT.

1. 36

2. 7

3. 15

4. 35

Q.

In a parallelogram ABCD, E and F are any two points on the sides AB and BC respectively. If ar ( ∆DCE) is 12 cm², then ar(∆ ADF) is

1. 6 cm²

2. 18 cm²

3. 3 cm²

4. 12 cm²

Q. The given figure shows parallelogram ABCD points P and Q price at the side a b then

Q.

AB and CD bisect each other at K . Poove that AC=BC

Q.

ABCD is a parallelogram in which E and F are the midpoints of the sides AB and CD respectively. BD is

1. BD = 3QP

2. BD = 4QP

3. BD = 2BP

4. BD = BQ

Q. P and Q are points on opposite sides AD and BC of a parallelogram ABCD, such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.

Q.

The diagonals of a parallelogram bisect each other.

1. True

2. False

Q. 23. ABCD is a quadrilateral in which AD=BC . if P, Q, R, S be the mid point of AB, AC, CD, and ND respectively, show that PQRS is a rhombus

Q. Given below is a parallelogram ABCD. Find the value of x and y.

1. 3 cm, 4 cm
2. 2 cm, 4 cm
3. 1 cm, 2 cm
4. 4 cm, 6 cm

Q. ABCD is a parallelogram with AC and BD as diagonals,
intersecting each other at O.
If AC = 12 cm, then AO = .

1. 5 cm
2. 3 cm
3. 12 cm
4. 6 cm

Q. Given below is a parallelogram ABCD. Find the value of x and y.

1. 1 cm, 2 cm
2. 2 cm, 4 cm
3. 3 cm, 4 cm
4. 4 cm, 6 cm

Q. ABCD is a parallelogram where AC and BD are the two diagonals. If BD is 6 cm more than AC and AE = 5 cm, find the length of BE.

Q. Given below is a parallelogram ABCD. Find the value of x and y.

1. 1 cm, 2 cm
2. 2 cm, 4 cm
3. 4 cm, 6 cm
4. 3 cm, 4 cm

Q. PQRS is a parallleogram, then PR ___ QS

1. perpendicular
2. parallel
3. bisects
4. not equal to

Q. Question 1
Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3cm and OD = 2cm, determine the lengths of AC and BD.

Q. In the given parallelogram ABCD, ∠ D = 63 °.

1. True
2. False

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

Q.

In which of the following quadrilaterals, diagonals bisect each other?

i) Parallelogram

ii) Rhombus

iii) Rectangle

iv) Square

v) Kite

1. i, ii, iii, iv

2. i, ii

3. ii, iv

4. All of them.

Q. The line segments joining the midpoints of the sides of a triangle form four triangles each of which is:

1. similar to the original triangle
2. congruent to the original triangle
3. an equilateral triangle
4. an isosceles triangle

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

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

Q. Given below is a parallelogram ABCD. Find the value of x and y.

1. 3 cm, 4 cm
2. 4 cm, 6 cm
3. 1 cm, 2 cm
4. 2 cm, 4 cm

Q. ABCD is a parallelogram where AC and BD are the two diagonals. If BD is 6 cm more than AC and AE = 5 cm, find the length of BE.

Q.

Assertion : In $\Delta ABC$, median AD is produced to X such that AD = DX. Then, ABXC is a parallelogram.
Reason : Diagonals AX and BC bisect each other at right angles.
Which of the following is correct?

1. If both assertion and reason are true and reason is the correct explanation of assertion
2. If both assertion and reason are true but reason is not the correct explanation of assertion
3. If assertion is true but reason is false
4. If assertion is false but reason is true

Q. Consider a parallelogram ABCD with diagonals AC = 12 cm and BD = 16 cm. What is the length of AD if the perimeter of triangle AOD is 25 cm?

1. 11 cm
2. 12 cm
3. 13 cm
4. 14 cm