Use side lengths, angles and diagonals to identify and compare quadrilaterals. These MCQs with answers and explanations support revision of Class 8 Maths, Ganita Prakash Part 1, Chapter 4: Quadrilaterals. The questions cover rectangles, squares, parallelograms, rhombuses, kites and trapeziums, including figures formed by joining triangles. Each solution explains which geometric property determines a missing angle, a length, a perimeter or a shape’s classification.
Class 8 Maths Ganita Prakash Part 1 Chapter 4 MCQs with Answers
Set 1: Quadrilateral Basics and Rectangles MCQs (Questions 1–5)
Q1. Which description always represents a quadrilateral?
[A]. A figure with four sides, one of which is curved
[B]. A closed figure made of three straight sides
[C]. An open figure made of four straight segments
[D]. A closed figure made of four straight sides
Q2. The diagonals AC and BD of rectangle ABCD intersect at O. If AC = 8 cm, what are BD and BO?
[A]. BD = 8 cm, BO = 8 cm
[B]. BD = 16 cm, BO = 8 cm
[C]. BD = 4 cm, BO = 2 cm
[D]. BD = 8 cm, BO = 4 cm
Q3. Two line segments of length 8 cm cross at their common midpoint at an angle of 40°. Their four endpoints are joined in order around the outside. Which description fits the resulting quadrilateral?
[A]. A rectangle that is not a square
[B]. rhombus that is not a rectangle
[C]. quadrilateral with no parallel sides
[D]. square
Q4. In rectangle PQRS, the diagonals PR and QS intersect at O. If ∠QOR = 110°, what is ∠OQR?
[A]. 110°
[B]. 70°
[C]. 35°
[D]. 55°
Q5. In rectangle ABCD, the diagonal AC makes ∠CAB = 30°. What is ∠CAD?
[A]. 60°
[B]. 120°
[C]. 90°
[D]. 30°
Set 2: Squares and Quadrilateral Angles MCQs (Questions 6–10)
Q6. In square ABCD, diagonal AC is drawn. What is ∠BAC?
[A]. 45°
[B]. 30°
[C]. 90°
[D]. 60°
Q7. PL and AM are perpendicular diameters of the same circle. The endpoints are joined in the order A, P, M, L. What is the most specific name for APML?
[A]. A rectangle that is not a square
[B]. A rhombus that is not a square
[C]. A square
[D]. A kite with unequal diagonals
Q8. A quadrilateral has three interior angles of 90° each. What must its fourth angle be?
[A]. 90°
[B]. 60°
[C]. 180°
[D]. 120°
Q9. Three interior angles of a quadrilateral are 60°, 70° and 120°. What is the fourth angle?
[A]. 130°
[B]. 120°
[C]. 110°
[D]. 100°
Q10. In parallelogram ABCD, ∠A = 30°. What are ∠B, ∠C and ∠D, respectively?
[A]. 150°, 30°, 150°
[B]. 30°, 150°, 30°
[C]. 150°, 150°, 30°
[D]. 90°, 150°, 90°
Set 3: Parallelogram and Rhombus Properties MCQs (Questions 11–15)
Q11. Adjacent sides of a parallelogram are 4 cm and 5 cm. What is its perimeter?
[A]. 18 cm
[B]. 16 cm
[C]. 20 cm
[D]. 9 cm
Q12. A parallelogram has diagonals of lengths 7 cm and 5 cm. What are the lengths of the two parts into which their intersection divides the 7 cm diagonal?
[A]. 2.5 cm and 2.5 cm
[B]. 3 cm and 4 cm
[C]. 3.5 cm and 3.5 cm
[D]. 7 cm and 7 cm
Q13. A parallelogram has an interior angle of 30°. Why is it not a rectangle?
[A]. A parallelogram cannot have diagonals
[B]. A rectangle cannot have parallel opposite sides
[C]. A rectangle must have four right angles
[D]. A parallelogram cannot have equal opposite sides
Q14. In rhombus ABCD, ∠A = 50° and diagonal BD is drawn. What is ∠ABD?
[A]. 25°
[B]. 65°
[C]. 50°
[D]. 130°
Q15. A rhombus has diagonals of lengths 4 cm and 5 cm. At what angle must the diagonals intersect?
[A]. 40°
[B]. 90°
[C]. 50°
[D]. 140°
Set 4: Rhombuses, Kites and Joined Triangles MCQs (Questions 16–20)
Q16. In rhombus XWVU, diagonal XV is drawn and ∠UVX = 30°. What is the interior angle at W?
[A]. 30°
[B]. 120°
[C]. 150°
[D]. 60°
Q17. On a geoboard, two equal perpendicular diagonals bisect each other. One diagonal is then extended by 2 cm at each end, while the other remains unchanged. After joining the four new endpoints in order, what is formed?
[A]. A square
[B]. A quadrilateral whose diagonals do not bisect each other
[C]. A rectangle that is not a square
[D]. A rhombus that is not a square
Q18. Two equilateral triangles, each with side length 8 cm, are joined along one complete side, with their interiors on opposite sides of that side. What is the perimeter of the resulting quadrilateral?
[A]. 32 cm
[B]. 24 cm
[C]. 48 cm
[D]. 40 cm
Q19. Two congruent isosceles triangles with sides 8 cm, 8 cm and 6 cm are joined along their 6 cm sides, on opposite sides of the shared side. Which statement about the resulting quadrilateral is correct?
[A]. Its perimeter is 28 cm
[B]. Its boundary sides alternate between 8 cm and 6 cm
[C]. All four boundary sides are 8 cm, so it is a rhombus
[D]. It has exactly one pair of equal adjacent sides
Q20. Two congruent triangles with sides 6 cm, 9 cm and 12 cm are joined along their 12 cm sides as mirror images on opposite sides of that side. What is the perimeter of the kite formed?
[A]. 24 cm
[B]. 30 cm
[C]. 54 cm
[D]. 36 cm
Set 5: Kite and Trapezium Properties MCQs (Questions 21–25)
Q21. In a convex kite ABCD, AB = BC and CD = DA. Diagonals AC and BD intersect at O. If AC = 6 cm, which pair of values is correct?
[A]. AO = 3 cm and ∠AOB = 90°
[B]. AO = 6 cm and ∠AOB = 90°
[C]. AO = 6 cm and ∠AOB = 45°
[D]. AO = 3 cm and ∠AOB = 45°
Q22. In a convex kite ABCD, AB = BC and CD = DA. If ∠ABC = 100°, what is ∠ABD?
[A]. 40°
[B]. 100°
[C]. 50°
[D]. 80°
Q23. In trapezium PQRS, PQ ∥ SR, ∠S = 135° and ∠R = 105°. What are ∠P and ∠Q, respectively?
[A]. 105° and 135°
[B]. 75° and 45°
[C]. 135° and 105°
[D]. 45° and 75°
Q24. In isosceles trapezium ABCD, AB ∥ CD, AD = BC, and AD is not parallel to BC. If ∠A = 100°, what is ∠C?
[A]. 100°
[B]. 80°
[C]. 180°
[D]. 40°
Q25. A trapezium is defined as a quadrilateral with at least one pair of parallel opposite sides. Which statement follows from this definition?
[A]. No rectangle is a trapezium
[B]. Every parallelogram is a trapezium
[C]. Every trapezium is a parallelogram
[D]. Only squares are trapeziums
Set 6: Quadrilateral Classification and Diagonals MCQs (Questions 26–30)
Q26. A kite has two non-overlapping pairs of equal adjacent sides. Which quadrilateral is both a kite and a rectangle?
[A]. A rhombus with an angle of 50°
[B]. A trapezium with exactly one pair of parallel sides
[C]. A rectangle with unequal adjacent sides
[D]. A square
Q27. Which statement correctly describes a quadrilateral that is both a kite and a parallelogram?
[A]. It must have exactly one pair of parallel sides
[B]. It must have four equal sides
[C]. Its diagonals cannot be perpendicular
[D]. It must have four right angles
Q28. The midpoints of the four sides of a square are joined consecutively. What is the most specific name for the inner quadrilateral?
[A]. A kite with unequal adjacent side lengths
[B]. A trapezium with exactly one pair of parallel sides
[C]. A rectangle that is not a square
[D]. A square
Q29. A quadrilateral has four equal sides and one interior angle of 90°. What is the most specific name for it?
[A]. A rhombus that is not a rectangle
[B]. A kite that is not a parallelogram
[C]. A square
[D]. A rectangle with unequal adjacent sides
Q30. Which statement about diagonals is NOT always true?
[A]. The diagonals of a square are perpendicular
[B]. The diagonals of a parallelogram bisect each other
[C]. The diagonals of a rectangle are equal
[D]. A quadrilateral with perpendicular diagonals must be a rhombus
Part 1 Chapter 4: Full Chapter MCQs (Set 1)
Q31. From which Latin words is “quadrilateral” derived?
[A]. ‘quadr’ meaning straight and ‘latus’ meaning line
[B]. ‘quadri’ meaning four and ‘latus’ referring to sides
[C]. ‘quadri’ meaning angle and ‘latus’ referring to four
[D]. ‘quad’ meaning square and ‘latus’ meaning angle
Q32. What are the two defining conditions for a quadrilateral to be called a rectangle?
[A]. All sides are equal and all angles are 90°.
[B]. Opposite sides are parallel and diagonals are equal.
[C]. All angles are 90° and opposite sides are of equal length.
[D]. Adjacent sides are equal and diagonals bisect each other.
Q33. If a carpenter needs to form a rectangle using two strips of wood as diagonals, and one strip is 8 cm long, what should be the length of the other strip?
[A]. Less than 8 cm
[B]. More than 8 cm
[C]. Exactly 8 cm
[D]. It can be any length
Q34. What does it mean for diagonals of a quadrilateral to “bisect each other”?
[A]. They divide the quadrilateral into two equal triangles.
[B]. They are of equal length.
[C]. They divide each other into two equal parts.
[D]. They are perpendicular to each other.
Part 1 Chapter 4: Full Chapter MCQs (Set 2)
Q35. What is a “conjecture” in geometric reasoning?
[A]. A statement derived through formal deduction only.
[B]. A statement about which we are highly confident but not yet sure if it always holds true.
[C]. An observation that is always incorrect.
[D]. A proven theorem that always holds true.
Q36. A simplified definition of a rectangle states that it is a quadrilateral in which all the angles are 90°. What else can be concluded about its opposite sides from this definition?
[A]. They intersect at 90°.
[B]. They are always parallel but not necessarily equal.
[C]. They must have equal lengths.
[D]. They are always unequal.
Q37. Which property states that when the sum of the internal angles on the same side of a transversal is 180°, the lines are parallel?
[A]. Angle sum property of a quadrilateral
[B]. Vertically opposite angles property
[C]. Transversal properties for parallel lines
[D]. Congruence property
Q38. How is the relationship between squares and rectangles represented using a Venn diagram?
[A]. Two separate, non-overlapping circles.
[B]. A rectangle circle completely inside a square circle.
[C]. A square circle completely inside a rectangle circle.
[D]. Two overlapping circles with a shared region.
Part 1 Chapter 4: Full Chapter MCQs (Set 3)
Q39. What additional condition is needed for the diagonals of a rectangle to form a square?
[A]. They must be longer than the sides.
[B]. They must be perpendicular to each other.
[C]. They must be parallel to each other.
[D]. They must not bisect each other.
Q40. What is a unique property of the diagonals of a square, not necessarily true for all rectangles?
[A]. They are of equal length.
[B]. They bisect each other.
[C]. They divide the angles of the square into equal halves.
[D]. They form isosceles triangles.
Q41. What is the sum of all angles in any quadrilateral?
[A]. 180°
[B]. 270°
[C]. 360°
[D]. 540°
Q42. What type of quadrilateral has parallel opposite sides but is not necessarily a rectangle?
[A]. Parallelogram
[B]. Rhombus
[C]. Trapezium
[D]. Square
Part 1 Chapter 4: Full Chapter MCQs (Set 4)
Q43. In a parallelogram, what is the sum of adjacent angles?
[A]. 180°
[B]. 360°
[C]. 270°
[D]. 90°
Q44. What can be said about the opposite angles of a parallelogram?
[A]. They are always right angles.
[B]. They are always equal.
[C]. They are never equal.
[D]. They add up to 180°.
Q45. What is the definition of a rhombus?
[A]. A quadrilateral with all angles equal to 90°.
[B]. A quadrilateral in which all the sides have the same length.
[C]. A quadrilateral with at least one pair of parallel opposite sides.
[D]. A quadrilateral with two non-overlapping adjacent pairs of sides having the same length.
Q46. What is the relationship between a square, a rectangle, a rhombus, and a parallelogram as shown in the Venn diagram?
[A]. A square is a type of rectangle and a type of rhombus, both of which are types of parallelograms.
[B]. A rhombus is a type of rectangle.
[C]. A rectangle is a type of rhombus.
[D]. A parallelogram is a type of square.
Part 1 Chapter 4: Full Chapter MCQs (Set 5)
Q47. What is a property of the diagonals of a rhombus concerning their intersection angle?
[A]. They are equal.
[B]. They bisect each other at any angle.
[C]. They intersect each other at an angle of 90°.
[D]. They do not bisect each other.
Q48. What is a “kite” defined as?
[A]. A quadrilateral with four equal sides.
[B]. A quadrilateral with two non-overlapping adjacent pairs of sides having the same length.
[C]. A quadrilateral with all angles equal to 90°.
[D]. A quadrilateral with exactly one pair of parallel sides.
Q49. What is a “trapezium” defined as?
[A]. A quadrilateral with two pairs of parallel opposite sides.
[B]. A quadrilateral with all angles equal to 90°.
[C]. A quadrilateral with at least one pair of parallel opposite sides.
[D]. A quadrilateral with equal non-parallel sides.
Q50. In an isosceles trapezium, what is true about the angles opposite to the equal sides?
[A]. They are always unequal.
[B]. They are always equal.
[C]. They add up to 180°.
[D]. They are always 90°.
Compare Properties Before Naming a Shape
Make a short comparison table for equal sides, parallel sides, angles and diagonals. Keep equal diagonals, perpendicular diagonals and diagonals that bisect each other as separate properties. When finding angles, state the relevant angle-sum or bisection rule. For classification questions, apply the stated definitions and check whether a shape belongs to more than one group.
