Quadrilaterals — Hard

Q1. The four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The measure of the largest angle is

• A. 108°
• B. 120°
• C. 144°
• D. 150°

Q2. Statement I: A rhombus in which one angle is 90° is a square. Statement II: A rectangle in which one pair of adjacent sides is equal is a square. Which of the following is correct?

• A. Only Statement I is true
• B. Only Statement II is true
• C. Both Statements I and II are true
• D. Neither Statement I nor Statement II is true

Q3. Assertion (A): In every parallelogram, the diagonals bisect each other. Reason (R): In every parallelogram, the diagonals are equal in length.

• 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

Q4. Consider these statements about a trapezium (): I. Every parallelogram is a trapezium. II. Every trapezium is a parallelogram. III. Every rectangle is a trapezium. Which of the following is correct?

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q5. A student claims: 'If the diagonals of a quadrilateral are equal AND bisect each other, the quadrilateral must be a square.' Using the deductions in the chapter, this claim is

• A. Correct — equal-and-bisecting diagonals force a square
• B. Incorrect — those two conditions only force a rectangle; a square also needs perpendicular diagonals
• C. Correct — but only when one angle is also 90°
• D. Incorrect — those conditions do not even force a rectangle

Q6. In parallelogram ABCD, ∠A = 65°. Using the parallelogram angle properties , the sum ∠B + ∠C is

• A. 115°
• B. 130°
• C. 180°
• D. 245°

Q7. PQRS is a kite in which PQ = PS and RQ = RS (). Which of the following statements about its diagonals is TRUE?

• A. Both diagonals are equal in length
• B. Both diagonals bisect each other
• C. The diagonals are perpendicular to each other
• D. Both diagonals bisect all four interior angles

Q8. In quadrilateral ABCD, ∠A = 70° and ∠B = 110°. If the remaining two angles ∠C and ∠D are equal to each other, the measure of ∠C is

• A. 70°
• B. 80°
• C. 90°
• D. 110°

Q9. In rhombus ABCD, diagonal BD is drawn. If ∠ABD = 35°, then ∠ABC is

• A. 35°
• B. 55°
• C. 70°
• D. 110°

Q10. A Class 8 pupil says: 'A trapezium can never be a parallelogram because a trapezium has exactly one pair of parallel sides.' definition shows this pupil has

• A. Stated the definition correctly
• B. Confused 'at least one pair' with 'exactly one pair'
• C. Confused the trapezium with the kite
• D. Forgotten that the diagonals of a trapezium are equal

Q11. Statement A: Every square is a rhombus. Statement B: Every rhombus is a square. Which of the following is correct according to and 100?

• A. A is true, B is true
• B. A is true, B is false
• C. A is false, B is true
• D. A is false, B is false

Q12. A Class 8 teacher asks her pupils to measure the diagonals of 1000 different rectangles. Every time the two diagonals come out equal. Following the chapter's reasoning, the BEST conclusion from this exercise is

• A. It is now proved that the diagonals of every rectangle are equal
• B. It is a strong conjecture; the universal claim still needs a deductive proof like Deduction 1
• C. It proves the result only for rectangles smaller than 10 cm
• D. It disproves Deduction 1

Q13. Consider the claim 'every square is a rectangle' using the analogy: a Malayali is Indian, but an Indian need not be Malayali. The point of this analogy in a Class 8 classroom is to show that

• A. Squares and rectangles have no shared properties
• B. A smaller, more specific set is contained inside a larger, more general set
• C. Indian shapes are squares and foreign shapes are rectangles
• D. A square is the same figure as a rectangle

Q14. Which of the following is the correct relationship between a kite and a rhombus, based and 105?

• A. Every kite is a rhombus and every rhombus is a kite
• B. Every rhombus is a kite, but every kite is not a rhombus
• C. Every kite is a rhombus, but every rhombus is not a kite
• D. A kite and a rhombus have nothing in common

Q15. In trapezium ABCD, AB ∥ CD. If ∠A = 75°, then ∠D is

• A. 15°
• B. 75°
• C. 105°
• D. 115°