Mastery

Quadrilaterals — Mastery

30 questions 30 min Full-chapter mastery

Q1. In any quadrilateral, the term 'vertex' refers to
- A. The point where two adjacent sides meet
- B. The midpoint of any side
- C. The point where the two diagonals cross
- D. The longest side of the figure
Q2. A Class 8 teacher is starting the Quadrilaterals chapter. Which of these is the BEST first classroom activity, in the spirit of the chapter's opening?
- A. Dictating the definition of every special quadrilateral on day one
- B. Solving twenty ratio-based angle problems first
- C. Asking pupils to memorise the angle-sum result before any examples
- D. Showing five figures and asking pupils which are quadrilaterals and why
Q3. Rohit lists three properties of every rectangle: (i) all angles are 90°, (ii) opposite sides are equal, (iii) opposite sides are parallel. Which of these are TRUE for every rectangle?
- A. (i) and (ii) only
- B. (i) and (iii) only
- C. (ii) and (iii) only
- D. (i), (ii) and (iii)
Q4. Assertion (A): The sum of the four interior angles of a concave (arrowhead-shaped) quadrilateral is also 360°. Reason (R): Any quadrilateral can be split into two triangles by drawing one diagonal, each triangle having angle sum 180°.
- 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, R is false
- D. A is false, R is true
Q5. On, the chapter argues that a rhombus is also a parallelogram. The reason given is
- A. Because the diagonals of a rhombus are perpendicular
- B. Because every rhombus has at least one right angle
- C. Because the diagonals bisect the angles of a rhombus
- D. Because all four sides of a rhombus are equal, in particular opposite sides are equal AND parallel
Q6. A pupil concludes: 'Any quadrilateral with two equal diagonals must be a rectangle.' Which counter-example from this chapter BEST shows the conclusion is wrong?
- A. A square — its diagonals are equal, but it is a special case of a rectangle
- B. A rhombus — its diagonals are equal
- C. A kite — its diagonals are equal
- D. An isosceles trapezium — its diagonals are equal but it is not a rectangle
Q7. In parallelogram PQRS, PQ = 7 cm and QR = 4 cm. Using Deduction 7 the lengths of RS and SP respectively are
- A. 7 cm and 4 cm
- B. 4 cm and 7 cm
- C. 7 cm and 7 cm
- D. 4 cm and 4 cm
Q8. From the Venn diagram which is the SMALLEST set among the following that contains the square?
- A. Parallelograms
- B. Trapeziums
- C. Quadrilaterals
- D. Rectangles ∩ Rhombuses (figures that are both rectangle and rhombus)
Q9. Three interior angles of a quadrilateral are 85°, 95° and 70°. The exterior angle at the fourth vertex (the angle that forms a linear pair with the fourth interior angle) measures
- A. 70°
- B. 110°
- C. 180°
- D. 290°
Q10. Two identical equilateral triangles, each of side 6 cm, are placed so that one common side fully coincides and the triangles lie on opposite sides of it. The resulting quadrilateral is
- A. A square
- B. A trapezium that is not a parallelogram
- C. A rectangle 6 cm by 12 cm
- D. A rhombus with each side 6 cm
Q11. In rectangle ABCD the diagonals AC and BD meet at O. The statement 'AC and BD bisect each other at O' means
- A. AC is twice as long as BD
- B. OA = OC and OB = OD
- C. AC is perpendicular to BD
- D. OA = OB = OC = OD
Q12. In the proof that ∠A + ∠B = 180° in parallelogram ABCD, side AB is treated as
- A. A diagonal of the parallelogram
- B. A transversal cutting the parallel lines AD and BC
- C. An axis of symmetry of the figure
- D. A radius of an inscribed circle
Q13. In quadrilateral ABCD, the pair of sides AB and CD is called
- A. Adjacent sides
- B. Opposite sides
- C. Diagonal sides
- D. Equal sides
Q14. A trapezium is called 'isosceles' when
- A. The two non-parallel sides are equal
- B. The two parallel sides are equal
- C. All four sides are equal
- D. The diagonals are perpendicular
Q15. In the chapter's vocabulary , a 'conjecture' is BEST described as
- A. A statement that has already been proved by a deduction
- B. A definition fixed by NCERT for a special quadrilateral
- C. A statement that looks true from examples but has not yet been proved
- D. A statement that has been disproved by a counter-example
Q16. Two teachers are deciding how to convince Class 8 pupils that the diagonals of every rectangle are equal. Teacher A asks pupils to measure ten different rectangles and tabulate the readings; Teacher B asks pupils to follow Deduction 1 step by step. Which choice BEST matches the chapter's intention?
- A. Teacher A alone — measurement is enough to settle a universal claim
- B. Teacher B alone — only a deduction proves the result for every rectangle
- C. Teacher A first to form the conjecture, then Teacher B to prove it for every rectangle
- D. Neither, because the result is given as a definition
Q17. Why does the chapter say that every rectangle is also a parallelogram?
- A. Because the diagonals of a rectangle are equal
- B. Because opposite sides of a rectangle are parallel, which is exactly the parallelogram condition
- C. Because every rectangle has four right angles
- D. Because the diagonals of a rectangle bisect each other
Q18. Kite ABCD has AB = AD and CB = CD (so AC is the line of symmetry). If ∠BAC = 28°, then ∠BAD equals
- A. 14°
- B. 28°
- C. 56°
- D. 62°
Q19. The 'Carpenter's Problem' opens the chapter to show that
- A. Geometry results have no real-life use
- B. Carpenters can always work without measurement
- C. An everyday workshop task — checking that a frame is truly rectangular — rests on a deductive geometric property
- D. Rectangles can only be built using rulers, never strings
Q20. While proving that the four angles of a quadrilateral add to 360°, which previously-known result does the chapter ASSUME and use?
- A. The exterior angle of a polygon is 360°
- B. Opposite sides of a rectangle are equal
- C. The three angles of any triangle add to 180°
- D. The diagonals of a quadrilateral bisect each other
Q21. A teacher gives each child two identical isosceles triangles (with sides 5 cm, 5 cm, 7 cm). When the 7 cm base of one triangle is fully joined to the 7 cm base of the other, with the triangles on opposite sides, the quadrilateral formed has sides
- A. 5 cm, 5 cm, 5 cm, 5 cm — so it is a rhombus
- B. 5 cm, 5 cm, 7 cm, 7 cm — so it is a kite-style figure with two pairs of adjacent equal sides
- C. 7 cm, 5 cm, 7 cm, 5 cm — so it is a parallelogram
- D. 5 cm, 7 cm, 5 cm, 7 cm — so it is a rectangle
Q22. Sara draws rectangle ABCD with AB = 6 cm and BC = 6 cm. Which of these conclusions follows from the chapter ?
- A. ABCD is only a rectangle, not a square, because the angles need to be checked separately
- B. ABCD is a square because its angles are 90° (it is a rectangle) AND all its sides are equal (since AB = BC and the opposite sides of a rectangle are equal too)
- C. ABCD cannot exist because a rectangle must have unequal adjacent sides
- D. ABCD is a rhombus but not a square
Q23. Reflecting on the chapter's 'Note to the Teacher' , which classroom prompt BEST builds the deductive habit that the chapter wants?
- A. Memorise the ten deductions and reproduce them word-for-word
- B. Whenever a pupil states a property, ask 'Can you justify it from a result we already know?'
- C. Always insist on a fresh measurement before any geometric claim
- D. Replace all proofs with neatly drawn figures
Q24. Following the construction outline a pupil draws parallelogram ABCD with AB = 5 cm, AD = 4 cm and ∠A = 30°. Using Deduction 7, the length of side CD is
- A. 3 cm
- B. 4 cm
- C. 5 cm
- D. 9 cm
Q25. A teacher hands out geoboards and rubber bands. Pupils stretch rubber bands across the diagonals so that the diagonals are equal in length, meet at their midpoints AND are perpendicular. The hands-on activity is BEST suited to lead pupils to the conclusion that
- A. The figure must be any parallelogram
- B. The figure must be a square (Deduction 5
- C. The figure must be a kite
- D. The figure must be an isosceles trapezium
Q26. A teacher wants to lead Class 8 pupils, in the correct sequence, to the result that the diagonals of a rhombus are perpendicular. Which of these orderings BEST matches the chapter's flow (Sections 4.3 and 4.4)?
- A. Define rhombus → measure many rhombuses → declare diagonals perpendicular
- B. Define rhombus → show it is a parallelogram → use congruent triangles formed by the diagonals to prove diagonals meet at 90° (Deduction 10)
- C. Define rhombus → assume diagonals are perpendicular → derive that all sides are equal
- D. Define square → call the square a rhombus → claim the property only for squares
Q27. In quadrilateral PQRS, ∠P = 100°, ∠Q = 80°, ∠R = 100° and ∠S = 80°. Which is the BEST description of PQRS using the chapter's results?
- A. Just an ordinary quadrilateral — no special name applies
- B. A parallelogram, because opposite angles are equal and adjacent angles add to 180° as on
- C. A rectangle, because the angles sum to 360°
- D. A rhombus, because the angles sum to 360°
Q28. Quadrilaterals by pointing out familiar shapes from everyday life. The chapter says that two such familiar four-sided shapes pupils have already met are
- A. Triangle and pentagon
- B. Rectangle and square
- C. Circle and oval
- D. Hexagon and octagon
Q29. Three figures are given: I — a parallelogram with sides 6 cm, 4 cm, 6 cm, 4 cm; II — a quadrilateral with exactly one pair of parallel sides 5 cm and 8 cm and non-parallel sides 3 cm and 4 cm; III — a kite with sides 5 cm, 5 cm, 7 cm, 7 cm. According to definition, which of these is/are trapeziums?
- A. Only II
- B. I and II only
- C. II and III only
- D. All three
Q30. Quadrilateral KITE has all four sides 5 cm long, all four angles 90° and both diagonals 5√2 cm long. Using the Venn hierarchy which is the MOST PRECISE name for KITE?
- A. Trapezium
- B. Parallelogram
- C. Rectangle
- D. Square

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