Class 9 Quadrilaterals Mock Test (CBSE)

Topics in Quadrilaterals

• What exactly is a quadrilateral
• Convex and non-convex quadrilaterals
• Properties of parallelograms
• Conditions for a quadrilateral to be a parallelogram
• Mid-point theorem and its converse
• Medians and the centroid of a triangle
• Varignon's theorem: the midpoint parallelogram
• Tiling the plane using any quadrilateral

Quadrilaterals practice questions with answers

1. Q1Multiple choice·1 mark
   Which of the following statements is true for a non-convex (concave) quadrilateral?

   1. (a)A quadrilateral in which each interior angle is strictly less than $180^\circ$.
   2. (b)A quadrilateral with all four sides equal and all angles $90^\circ$.
   3. (c)A quadrilateral in which at least one interior angle is greater than $180^\circ$.
   4. (d)A quadrilateral whose diagonals bisect each other at right angles.
   Show answer and step marks

   1. Correct option: (c) A quadrilateral in which at least one interior angle is greater than $180^\circ$.+1

   Answer: (c)
2. Q2Multiple choice·1 mark
   Which of the following describes the basic components of a simple quadrilateral?

   1. (a)It has 3 sides, 4 vertices, and 2 diagonals.
   2. (b)It has 4 sides, 4 vertices, and 4 diagonals.
   3. (c)It has 4 sides, 3 vertices, and 1 diagonal.
   4. (d)It has 4 sides, 4 vertices, and 2 diagonals.
   Show answer and step marks

   1. Correct option: (d) It has 4 sides, 4 vertices, and 2 diagonals. A simple quadrilateral is a closed polygon with 4 sides, 4 vertices, and exactly 2 diagonals.+1

   Answer: (d)
3. Q3Multiple choice·1 mark
   In triangle ABC, D and E are the mid-points of AB and AC respectively. If BC = $9.4$ cm, what is the length of DE?

   1. (a)$9.4$ cm
   2. (b)$2.35$ cm
   3. (c)$18.8$ cm
   4. (d)$4.7$ cm
   Show answer and step marks

   1. Correct option: (d) $4.7$ cm+1

   Answer: (d)
4. Q4Assertion and reason·1 mark
   Assertion (A): The centroid of a triangle divides each median in the ratio $2:1$, measured from the vertex. Reason (R): The three medians of a triangle are concurrent.

   1. (a)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
   2. (b)Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
   3. (c)Assertion (A) is true but Reason (R) is false.
   4. (d)Assertion (A) is false but Reason (R) is true.
   Show answer and step marks

   1. Correct option: (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).+1

   Answer: (b)
5. Q5Short answer·2 marks
   Regular polygons are compared for tiling the plane. (a) Find the measure of each interior angle of a regular octagon. [1] (b) Explain, with reason, why copies of any quadrilateral can be arranged to tile the plane with no gaps or overlaps. [1]
   Show answer and step marks

   1. (a) Interior angle of a regular polygon with n sides = $\frac{(n-2)\times 180^\circ}{n}$; for n = 8, this is $\frac{6\times 180^\circ}{8}$.+0.5
   2. (a) Each interior angle $= 135^\circ$.+0.5
   3. (b) A half-turn (180° rotation) about the midpoint of a side maps the quadrilateral onto a copy that shares that whole side exactly, because the midpoint swaps the two ends of the side.+0.5
   4. (b) Repeating this for every side, the copies fit edge to edge; the four angles of any quadrilateral add up to $360^\circ$, so the corners meet at each point with no gap or overlap.+0.5

   Answer: (a) Each interior angle is $135^\circ$. (b) A half-turn about the midpoint of each side gives a copy sharing that whole side; the copies fit edge to edge, and the corner angles total $360^\circ$, so there are no gaps or overlaps.
6. Q6Short answer·2 marks
   In quadrilateral $ABCD$, $P$, $Q$, $R$ and $S$ are the mid-points of $AB$, $BC$, $CD$ and $DA$ respectively. Given that $AC = 8$ cm, $BD = 6$ cm and $AC \perp BD$. (a) Find the length of $PQ$. [1] (b) Name the quadrilateral $PQRS$ and justify your answer. [1]
   Show answer and step marks

   1. In $\triangle ABC$, $P$ and $Q$ are mid-points of $AB$ and $BC$, so by the mid-point theorem $PQ = \frac{1}{2}AC = \frac{1}{2}(8) = 4$ cm.+1
   2. $PQ \parallel AC$ and $QR \parallel BD$ (Varignon), so $PQ \perp QR$ as $AC \perp BD$; $PQRS$ is a parallelogram with one right angle, hence a rectangle.+1

   Answer: (a) $PQ = 4$ cm; (b) $PQRS$ is a rectangle.

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