Question Bank — Quadrilaterals

NCERT Class 8 Mathematics · Chapter 4 · CBSE Board Pattern

Class 8 Mathematics Chapter 4 Question Bank CBSE Board Pattern

QUESTION BANK

Chapter 4: Quadrilaterals

(Based strictly on NCERT Ganita Prakash Grade 8)

Section A — MCQs (10 questions, 1 mark each)

  1. A quadrilateral in which all angles are 90° must have
    (a) equal diagonals only
    (b) opposite sides equal
    (c) diagonals bisecting each other at 90°
    (d) all sides equal

  2. In a rectangle, the diagonals
    (a) are unequal and bisect each other
    (b) are equal and bisect each other
    (c) are equal and intersect at 90°
    (d) bisect the angles of the rectangle

  3. Which of the following is true for every rhombus?
    (a) Diagonals are equal
    (b) Diagonals bisect each other at right angles
    (c) All angles are 90°
    (d) Opposite sides are unequal

  4. The sum of all angles of any quadrilateral is
    (a) 180° (b) 270° (c) 360° (d) 540°

  5. A square is a special type of
    (a) parallelogram only (b) rectangle only
    (c) both rectangle and rhombus (d) trapezium only

Assertion-Reason Questions

  1. Assertion (A): The diagonals of a rectangle bisect each other.
    Reason (R): In a rectangle, the triangles formed by one diagonal are congruent by SAS.
    (a) Both A and R are true and R is the correct explanation of A.
    (b) Both A and R are true but R is not the correct explanation of A.
    (c) A is true but R is false.
    (d) A is false but R is true.

  2. Assertion (A): A quadrilateral with three angles equal to 90° must have the fourth angle also equal to 90°.
    Reason (R): The sum of the interior angles of any quadrilateral is 360°.
    (a) Both A and R are true and R is the correct explanation of A.
    (b) Both A and R are true but R is not the correct explanation of A.
    (c) A is true but R is false.
    (d) A is false but R is true.

  3. In a parallelogram, opposite angles are always
    (a) supplementary (b) complementary (c) equal (d) right angles

  4. The diagonals of a kite
    (a) always bisect each other at 90°
    (b) are always equal
    (c) one diagonal bisects the other at right angles and bisects two angles
    (d) never bisect any angle

  5. Which statement is correct?
    (a) Every trapezium is a parallelogram.
    (b) Every rhombus is a square.
    (c) Every square is a rectangle.
    (d) Every kite has all sides equal.

Section B — Very Short Answer (6 questions, 2 marks each)

  1. State the two different definitions of a rectangle given in the chapter.
  2. In a rectangle ABCD, if one diagonal is 8 cm, what is the length of the other diagonal? Give reason.
  3. What is the sum of adjacent angles of a parallelogram? Why?
  4. Name the quadrilateral in which (i) all sides are equal and diagonals bisect each other at 90°, (ii) diagonals are equal and bisect each other at 90°.
  5. In a rhombus, if one angle is 50°, find the remaining angles.
  6. Draw a rough diagram of an isosceles trapezium and mark one pair of equal sides and the base angles that are equal.

Section C — Short Answer (5 questions, 3 marks each)

  1. In rectangle ABCD, diagonals intersect at O. If ∠AOB = 60°, find all four angles formed at O.
  2. A parallelogram has one angle 30°. Find all its angles and justify using properties of parallel lines.
  3. In rhombus GAME, diagonal GE is drawn. If ∠AGE = 65°, find all angles of the rhombus.
  4. Two equilateral triangles of side 5 cm are joined along one side. What type of quadrilateral is formed? Find all its angles and sides.
  5. In quadrilateral ABCD, ∠A = 90°, ∠B = 90°, ∠C = 90°. Prove that it must be a rectangle (using the chapter deduction).

Section D — Long Answer (3 questions, 5 marks each)

  1. Using the diagonal properties, construct a rectangle whose diagonals are each 10 cm and intersect at 60°. Find all angles between the diagonals and justify that the figure is a rectangle. (Multi-step construction + justification)
  2. Prove that if the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a rectangle. (Use congruence as in Deduction 1 and 2)
  3. A carpenter has two strips of wood each 10 cm long. Explain, with justification, how he should join them at their midpoints so that the thread passing through the endpoints forms (i) a rectangle, (ii) a square. State the additional condition required for a square.

Section E — Case/Source-Based (2 questions, 4 marks each)

Case 1: Carpenter’s Frame

A carpenter wants to make a rectangular frame using two thin wooden strips as diagonals. He has one strip of length 12 cm.

(a) What should be the length of the second strip? (1 mark)
(b) At what point should the strips be joined? (1 mark)
(c) What should be the angle between the diagonals? Justify using chapter properties. (1 mark)
(d) If he instead wants a square frame, what extra condition must he satisfy? (1 mark)

Case 2: Farmer’s Base

A farmer in Mozambique wants to mark a rectangular base for a house using ropes. He fixes two ropes of equal length crossing at their midpoints.

(a) What type of quadrilateral will be formed if the ropes cross at 90°? (1 mark)
(b) If the ropes cross at 60°, will the base still have all angles 90°? Give reason. (1 mark)
(c) State two properties of the sides that will be satisfied. (1 mark)
(d) How does this method ensure opposite sides are parallel? (1 mark)

▶ Answer Key Attempt all questions first,
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Section A

  1. (b)
  2. (b)
  3. (b)
  4. (c)
  5. (c)
  6. (a)
  7. (a)
  8. (c)
  9. (c)
  10. (c)

Section B

  1. (i) All angles 90° and opposite sides equal. (ii) Diagonals equal and bisect each other.
  2. 8 cm (diagonals of rectangle are equal — 1 mark; corresponding parts of congruent triangles — 1 mark).
  3. 180° (consecutive interior angles on same side of transversal are supplementary).
  4. (i) Rhombus (ii) Square.
  5. 50°, 130°, 50°, 130° (opposite angles equal, adjacent angles supplementary).
  6. Diagram with UV = VW, base angles at U and V equal.

Section C

  1. All angles at O are 60°, 60°, 120°, 120° (vertically opposite + linear pair + isosceles triangles).
  2. 30°, 150°, 30°, 150° (adjacent supplementary, opposite equal).
  3. 50°, 130°, 50°, 130° (diagonal creates four equal base angles of 65° each; opposite angles equal).
  4. Rhombus (or square if angles become 90°); all sides 5 cm, all angles 60° or 120°.
  5. Join diagonal BD → ∆BAD ≅ ∆BCD by AAS (∠B = ∠D = 90°, ∠1 = ∠2) → opposite sides equal → rectangle.

Section D

  1. Construction steps + diagonals equal & bisect each other → all angles 90° (as proved in Deduction 3).
  2. Full congruence proof: diagonals equal + bisect each other → ∆AOB ≅ ∆COD (AAS) → all angles 90° and opposite sides equal.
  3. (i) Join at midpoints (equal diagonals bisecting each other). (ii) Additional condition: intersect at 90°.

Section E

Case 1

(a) 12 cm (diagonals equal).
(b) Midpoints (diagonals bisect each other).
(c) Any angle (all give 90° angles of rectangle).
(d) Diagonals must intersect at 90°.

Case 2

(a) Square (or rhombus).
(b) Yes (Deduction 3).
(c) Opposite sides equal and parallel.
(d) Opposite sides parallel by construction and transversal properties.

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All questions are answerable from the NCERT chapter text. Reviewed by GFIS faculty.