Rectilinear Figures – Quadrilaterals Quiz - ICSE Class 9 Mathematics

Free practice quiz: Rectilinear Figures – Quadrilaterals (ICSE Class 9 Mathematics). 59 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 9 Mathematics practice quiz has 59 multiple-choice questions on Rectilinear Figures – Quadrilaterals, and 59 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. In a parallelogram ABCD, if angle A = 110 degrees, then angle B is:

   1. 110 degrees
   2. 70 degrees
   3. 90 degrees
   4. 180 degrees
   Show answer

   Answer: B. 70 degrees

   In a parallelogram, consecutive angles are supplementary. Therefore, angle A + angle B = 180 degrees. Given angle A = 110 degrees, angle B = 180 - 110 = 70 degrees.

2. In a trapezium ABCD, AB || DC. If AD = BC, then it is:

   1. A parallelogram
   2. A rectangle
   3. An isosceles trapezium
   4. A rhombus
   Show answer

   Answer: C. An isosceles trapezium

   A trapezium with equal non-parallel sides is defined as an isosceles trapezium.

3. If the midpoints of the sides of a rectangle are joined in order, the resulting figure is a:

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

   Answer: B. Rhombus

   When the midpoints of the sides of any quadrilateral are joined in order, the resulting figure is a parallelogram. If the original quadrilateral is a rectangle, the diagonals of the rectangle are equal and bisect each other. Joining the midpoints of the sides of a rectangle results in a rhombus. This can be shown using midpoint theorem on triangles formed by diagonals.

4. If the interior angle of a regular polygon is 150 degrees, how many sides does it have?

   1. 10
   2. 12
   3. 15
   4. 18
   Show answer

   Answer: B. 12

   For a regular polygon with n sides, each interior angle is given by [(n-2) * 180] / n. We are given that each interior angle is 150 degrees. So, [(n-2) * 180] / n = 150. This simplifies to 180n - 360 = 150n. Rearranging, 180n - 150n = 360, which gives 30n = 360. Therefore, n = 360 / 30 = 12. The polygon has 12 sides.

5. If one of the angles of a parallelogram is 90 degrees, then it is a:

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

   Answer: C. Rectangle

   A parallelogram with one right angle has all its angles as right angles, making it a rectangle. A square is a special type of rectangle, but 'Rectangle' is the direct classification.

More questions in this quiz

Answers and explanations are in the full quiz.

1. The diagonals of a rhombus are perpendicular bisectors of each other. If one diagonal of a rhombus is 12 cm and the other is 16 cm, what is the length of each side?
2. A rectangle has a length of 15 cm and a breadth of 8 cm. What is the length of its diagonal?
3. In a trapezium ABCD, AB is parallel to DC. If angle A = angle B and angle C = angle D, what type of trapezium is it?
4. Which of the following is NOT a property of a square?
5. If the sum of opposite angles of a quadrilateral is 180 degrees each, the quadrilateral must be a:
6. In a kite ABCD, AB = AD and CB = CD. If angle A = 100 degrees and angle C = 60 degrees, what is angle B?
7. In a rhombus ABCD, if angle A = 100 degrees, then angle B is:
8. The sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. If a regular polygon has each interior angle equal to 144 degrees, how many sides does it have?
9. Which of the following quadrilaterals has all its diagonals bisecting each other at right angles?
10. If two adjacent angles of a parallelogram are in the ratio 2:3, what are the measures of the angles?
11. What is the sum of the exterior angles of any convex polygon?
12. If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a:
13. In a parallelogram PQRS, angle Q = 90 degrees. What type of parallelogram is it?
14. If one angle of a parallelogram is 30 degrees less than twice the adjacent angle, find the measure of the larger angle.
15. If one angle of a parallelogram is 24 degrees more than the adjacent angle, find the measure of the larger angle.
16. In a cyclic quadrilateral ABCD, angle A = 80 degrees and angle C = 95 degrees. What is the measure of angle B?
17. In a cyclic quadrilateral ABCD, if angle A = 80 degrees and angle B = 95 degrees, what is the measure of angle C?
18. In a parallelogram ABCD, the diagonals AC and BD intersect at O. If AO = 5 cm and BO = 7 cm, what is the length of diagonal BD?
19. Which of the following statements about a trapezium is FALSE?
20. In a square ABCD, if the length of the diagonal AC is 10√2 cm, what is the length of side AB?
21. A quadrilateral has angles measuring x, 2x, 3x, and 4x degrees. What is the value of x?
22. In a parallelogram ABCD, if angle A - angle B = 20 degrees, what is the measure of angle A?
23. The area of a rhombus is half the product of the lengths of its diagonals. If the diagonals are 10 cm and 12 cm, what is the area of the rhombus?
24. In a trapezium ABCD, AB || DC. If angle D = angle C and angle A = angle B, what kind of trapezium is it?
25. If the diagonals of a quadrilateral are perpendicular bisectors of each other, then the quadrilateral is a:
26. Which property does a square NOT share with a rhombus?
27. In a parallelogram ABCD, if angle A = 120 degrees, what is the measure of angle C?
28. If the perimeter of a square is 64 cm, what is the length of its diagonal?
29. In a kite PQRS, PQ = QR and RS = SP. If angle P = 100 degrees and angle R = 60 degrees, what is angle Q?
30. In a kite PQRS, PQ = SP and QR = RS. If angle P = 120 degrees and angle R = 80 degrees, what is angle Q?
31. The diagonals of a rectangle are 10 cm long. If the length of the rectangle is 8 cm, what is its breadth?
32. In a quadrilateral ABCD, if AB || DC and AD || BC, what type of quadrilateral is it?
33. The diagonals of a kite are perpendicular. If one diagonal is 10 cm and the other is 16 cm, what is the area of the kite?
34. In a parallelogram ABCD, angle B = 70 degrees. What is the measure of angle D?
35. If the midpoints of the sides of a rhombus are joined in order, the resulting figure is a:
36. In a cyclic quadrilateral ABCD, angle A + angle C = 180 degrees. If angle A = 80 degrees, what is angle C?
37. The sum of interior angles of a pentagon is:
38. In a trapezium ABCD, AB || DC. If AD = 5 cm, BC = 5 cm, and AB = 8 cm, DC = 12 cm, then the trapezium is:
39. If all angles of a quadrilateral are equal, it must be a:
40. In a parallelogram ABCD, if angle A = 60 degrees, then angle B is:
41. If the diagonals of a quadrilateral are equal and bisect each other at right angles, the quadrilateral is a:
42. A regular hexagon has interior angles of:
43. In a parallelogram ABCD, if diagonal AC = 10 cm and diagonal BD = 12 cm, and they intersect at O, what is the length of AO?
44. In an isosceles trapezium ABCD, AB || DC, AD = BC. If angle D = 70 degrees, what is angle A?
45. If the adjacent sides of a parallelogram are 8 cm and 6 cm, and one of its angles is 90 degrees, what is its area?
46. The sum of the angles subtended by the diagonals at the vertices of a quadrilateral is:
47. In a quadrilateral ABCD, AB = BC and CD = DA. This quadrilateral is a:
48. If a quadrilateral has diagonals that are equal and bisect each other, it is a:
49. In a parallelogram, if one angle is 110 degrees, the adjacent angles are:
50. Which of the following quadrilaterals has diagonals that are equal and bisect each other perpendicularly?
51. The sum of the exterior angles of a regular n-sided polygon is 360 degrees. If each exterior angle is 40 degrees, then the polygon is a:
52. In a parallelogram ABCD, if angle A = 100 degrees, then angle B is:
53. If the perimeter of a rectangle is 36 cm and its length is 12 cm, what is its breadth?
54. The diagonals of a rhombus are perpendicular bisectors of each other. If one diagonal is 16 cm and the side length of the rhombus is 10 cm, what is the length of the other diagonal?

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