### Examination Questions in Parallelograms

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1. Let ABCD be a parallelogram. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Consider the following statements:

- Area of triangle APS < Area of triangle DSR if BD < AC.
- Area of triangle ABC = 4 (Area of triangle BPQ).

Select the correct answer using the code given below:

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

2. Consider the following statements:

- Let ABCD be a parallelogram which is not a rectangle. Then 2(AB
^{2}+ BC^{2}) ≠ AC^{2}+ BD^{2} - If ABCD is a rhombus with AB = 4 cm, then AC
^{2}+ BD^{2}= n^{3}for some positive integer n.

Which of the above statements is/are correct?

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

3. ABCD is a parallelogram. E is a point on BC such that BE : EC = m : n. If AE and DB intersect in F, then what is the ratio of the area of triangle FEB to the area of triangle AFD?

- m/n
- (m/n)
^{2} - (n/m)
^{2} - [m/(m + n)]
^{2}

4. One side of a parallelogram is 8.06 cm and its perpendicular distance from opposite side is 2.08 cm. What is the approximate area of the parallelogram?

- 12.56 cm
^{2} - 14.56 cm
^{2} - 16.76 cm
^{2} - 22.56 cm
^{2}

5. Consider the following statements :

- If the diagonals of a parallelogram ABCD are perpendicular, then ABCD may be a rhombus.
- If the diagonals of a quadrilateral ABCD are equal and perpendicular, then ABCD is a square.

Which of the statements given above is/are correct?

- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2

6. ABCD is a parallelogram. If the bisectors of the angle A and angle C meet the diagonal BD at points P and Q respectively, then which one of the following is correct?

- PCQA is a straight line
- Triangle APQ is similar to triangle PCQ
- AP = CP
- AP = AQ

7. Let ABCD be a parallelogram. Let m, n be positive integers such that n < m < 2n. Let AC = 2mn and BD = m^{2} – n^{2}. Let AB = (m^{2} + n^{2})/2.

- Statement –I: AC > BD.
- Statement- II: ABCD is a rhombus.

Which one of the following is correct in respect of the above statements?

- Both statement-I and statement-II are true and statement-II is the correct explanation of statement-I
- Both statement-I and statement-II are true but statement-II is not the correct explanation of statement-I
- Statement-I is true, but statement-II is false
- Statement-II is true, but statement-I is false

8. The sides of a parallelogram are 12 cm and 8 cm long and one of the diagonals is 10 cm long. If d is the length of other diagonal, then which one of the following is correct?

- d < 8 cm
- 8 cm < d < 10 cm
- 10 cm < d < 12 cm
- d > 12 cm

9. Let LMNP be a parallelogram and NR be perpendicular to LP. If the area of the parallelogram is six times the area of triangle RNP and RP = 6 cm, what is LR equal to?

- 15 cm
- 12 cm
- 9 cm
- 8 cm

10. In the figure given above, ABCD is a parallelogram. P is a point on BC such that PB : PC = 1 : 2. DP produced meets AB produced at Q. If the area of the triangle BPQ is 20 square units, what is the area of the triangle DCP?

- 20 square units
- 30 square units
- 40 square units
- None of the above