Quadrilaterals MCQs for UPSC Prelims

120 practice questions covering Quadrilaterals, organised into 0 topics. 120 questions include a written explanation. Pick a topic below, or try the samples first.

Sample questions

Q1
medium

Consider these statements. (i) Every square is both a rectangle and a rhombus. (ii) Every rectangle is both a square and a rhombus. Which statement(s) are correct?

  1. A Neither (i) nor (ii)
  2. B Only (ii)
  3. C Only (i)
  4. D Both (i) and (ii)
Show answer and explanation

Correct answer: C - Only (i)

A square has four right angles, which makes it a rectangle, and four equal sides, which makes it a rhombus, so (i) is true. A rectangle measuring $7\ \text{cm}$ by $4\ \text{cm}$ is neither a square nor a rhombus, so (ii) is false. Only (i) holds.

Q2
medium

In parallelogram $PQRS$ the diagonals meet at the point $O$. If $PO=6\ \text{cm}$, how long is the diagonal $PR$?

  1. A $6\ \text{cm}$
  2. B $12\ \text{cm}$
  3. C $24\ \text{cm}$
  4. D $3\ \text{cm}$
Show answer and explanation

Correct answer: B - $12\ \text{cm}$

The diagonals bisect each other, so $O$ is the midpoint of $PR$ and $PR=2\times6=12\ \text{cm}$. Answering $6\ \text{cm}$ repeats the half instead of the whole. Halving again gives $3\ \text{cm}$, and doubling twice gives $24\ \text{cm}$.

Q3
medium

In quadrilateral $ABCD$ the diagonals cross at $O$, and it is found that $AO=OC$ and $BO=OD$. What can be concluded?

  1. A $ABCD$ is a kite
  2. B $ABCD$ is a rectangle
  3. C $ABCD$ is a parallelogram
  4. D Nothing can be concluded from this
Show answer and explanation

Correct answer: C - $ABCD$ is a parallelogram

Diagonals that bisect each other are exactly the test for a parallelogram, so $ABCD$ is one. It would be a rectangle only if the diagonals were also equal, which is not given. In a kite one diagonal bisects the other but is not itself bisected, so a kite is ruled out.

Q4
hard

Consider these statements. (i) Every rhombus is a parallelogram. (ii) Every parallelogram whose diagonals meet at right angles is a rhombus. Which statement(s) are correct?

  1. A Neither (i) nor (ii)
  2. B Only (ii)
  3. C Both (i) and (ii)
  4. D Only (i)
Show answer and explanation

Correct answer: C - Both (i) and (ii)

Four equal sides force both pairs of opposite sides to be parallel, so (i) is true. In a parallelogram the diagonals already bisect each other, and adding a right angle at the crossing makes all four sides come out equal, so (ii) is true too. Both statements therefore hold.

Q5
easy

What is always true of the diagonals of a parallelogram?

  1. A The two diagonals meet at right angles
  2. B Each diagonal cuts the other into two equal parts
  3. C The two diagonals are equal in length
  4. D Each diagonal cuts the corner angles into two equal parts
Show answer and explanation

Correct answer: B - Each diagonal cuts the other into two equal parts

In every parallelogram the diagonals bisect each other where they cross. Equal diagonals occur only in a rectangle, perpendicular diagonals only in a rhombus, and diagonals that bisect the corner angles only in a rhombus or a square.

Q6
medium

Assertion (A): In the quadrilateral family tree, a parallelogram is a special kind of square. Reason (R): A square has four equal sides and four right angles.

  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: D - A is false, but R is true

A is false, because the relationship runs the other way: a square is a parallelogram with extra conditions, while a slanted parallelogram is not a square at all. R states the defining properties of a square correctly. So the assertion fails while the reason stands.

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