CBSE Class 9 Mathematics Quadrilaterals MCQs Set 05

Mathematics Objective Questions and Answers: Chapter 08 Quadrilaterals

Explore reliable objective questions for Chapter 08 Quadrilaterals tailored for Class 9 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Download Chapter 08 Quadrilaterals MCQs with Answers

Access the complete set of multiple-choice questions for Chapter 08 Quadrilaterals below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: Three angles of a quadrilateral are \( 100^\circ,\ 98^\circ,\ 92^\circ \). The fourth angle is
(a) \( 70^\circ \)
(b) \( 80^\circ \)
(c) \( 60^\circ \)
(d) \( 90^\circ \)
Show Answer & Explanation

Answer: (a) \( 70^\circ \)

Explanation:
1. The angles of a quadrilateral add up to \( 360^\circ \).
2. \( 360-(100+98+92)=70^\circ \).

Teacher's Note:
1. Angle sum of a quadrilateral is 360 degrees.

Question 2: Three angles of a quadrilateral are \( 110^\circ,\ 50^\circ,\ 40^\circ \). The fourth angle is
(a) \( 150^\circ \)
(b) \( 160^\circ \)
(c) \( 200^\circ \)
(d) \( 120^\circ \)
Show Answer & Explanation

Answer: (b) \( 160^\circ \)

Explanation:
1. \( 360-(110+50+40)=160^\circ \).

Teacher's Note:
1. Subtract from 360 degrees.

Question 3: The angles \( A,B,C,D \) of a quadrilateral are in the ratio \( 1:2:4:5 \). The largest angle is
(a) \( 120^\circ \)
(b) \( 135^\circ \)
(c) \( 150^\circ \)
(d) \( 180^\circ \)
Show Answer & Explanation

Answer: (c) \( 150^\circ \)

Explanation:
1. \( 12k=360 \), so \( k=30 \).
2. The angles are \( 30^\circ,60^\circ,120^\circ,150^\circ \).

Teacher's Note:
1. Total 360 degrees shared in ratio.

Question 4: In quadrilateral \( ABCD \), \( CO \) and \( DO \) bisect \( \angle C \) and \( \angle D \) and meet at \( O \). If \( \angle A=100^\circ \) and \( \angle B=80^\circ \), then \( \angle COD \) is
(a) \( 180^\circ \)
(b) \( 100^\circ \)
(c) \( 45^\circ \)
(d) \( 90^\circ \)
Show Answer & Explanation

Answer: (d) \( 90^\circ \)

Explanation:
1. \( \angle C+\angle D=360-180=180^\circ \).
2. \( \angle COD=180-\frac12(\angle C+\angle D)=90^\circ \) (this equals \( \frac12(\angle A+\angle B) \)).

Teacher's Note:
1. Find half of C plus D.

Question 5: \( ABCD \) is a rectangle with vertex \( A \) at the centre of a circle of radius \( 10 \) cm, \( B \) and \( D \) on perpendicular radii and \( C \) on the circle. If \( AD=2\sqrt5 \) cm, the area of the rectangle is
(a) \( 40\text{ cm}^2 \)
(b) \( 20\text{ cm}^2 \)
(c) \( 80\text{ cm}^2 \)
(d) \( 20\sqrt5\text{ cm}^2 \)
Show Answer & Explanation

Answer: (a) \( 40\text{ cm}^2 \)

Explanation:
1. The diagonal \( AC \) is a radius, so \( AC=10 \).
2. \( AB=\sqrt{100-20}=\sqrt{80}=4\sqrt5 \).
3. Area \( =2\sqrt5\times4\sqrt5=40 \) cm\( ^2 \).

Teacher's Note:
1. The diagonal of the rectangle equals the radius.

Question 6: \( ABCD \) is a rhombus with \( \angle ABC=58^\circ \). Then \( \angle ACD \) is
(a) \( 58^\circ \)
(b) \( 61^\circ \)
(c) \( 29^\circ \)
(d) \( 122^\circ \)
Show Answer & Explanation

Answer: (b) \( 61^\circ \)

Explanation:
1. \( \angle BCD=180-58=122^\circ \) (adjacent angles of a parallelogram).
2. The diagonal \( AC \) bisects \( \angle BCD \), so \( \angle ACD=61^\circ \).

Teacher's Note:
1. Diagonals of a rhombus bisect its angles.

Question 7: The angle between the two altitudes of a parallelogram drawn from the vertex of an obtuse angle is \( 60^\circ \). The obtuse angle of the parallelogram is
(a) \( 100^\circ \)
(b) \( 150^\circ \)
(c) \( 120^\circ \)
(d) \( 135^\circ \)
Show Answer & Explanation

Answer: (c) \( 120^\circ \)

Explanation:
1. In the quadrilateral formed by the two altitudes and two sides, two angles are \( 90^\circ \), so the angle of the parallelogram plus the angle between the altitudes is \( 180^\circ \).
2. Obtuse angle \( =180-60=120^\circ \) (the other angles are \( 60^\circ \)).

Teacher's Note:
1. The quadrilateral has two right angles.

Question 8: In \( \triangle ABC \), \( P,Q,R \) are the mid-points of \( BC,CA,AB \). If \( AC=21 \) cm, \( BC=29 \) cm and \( AB=30 \) cm, the perimeter of the quadrilateral \( ARPQ \) is
(a) \( 80 cm \)
(b) \( 40 cm \)
(c) \( 60 cm \)
(d) \( 51 cm \)
Show Answer & Explanation

Answer: (d) \( 51 cm \)

Explanation:
1. \( AR=\frac12AB=15 \) and \( QA=\frac12AC=10.5 \).
2. By the mid-point theorem \( RP=\frac12AC=10.5 \) and \( PQ=\frac12AB=15 \).
3. Perimeter \( =15+10.5+15+10.5=51 \) cm.

Teacher's Note:
1. ARPQ is a parallelogram.

Question 9: The triangle formed by joining the mid-points of the sides of an isosceles triangle is
(a) \( isosceles \)
(b) \( equilateral \)
(c) \( scalene \)
(d) \( right-angled \)
Show Answer & Explanation

Answer: (a) \( isosceles \)

Explanation:
1. Each side of the mid-point triangle is half of a side of the original triangle, so two equal sides of the original give two equal sides in the new triangle.

Teacher's Note:
1. Mid-point theorem.

Question 10: The triangle formed by joining the mid-points of the sides of a right triangle is
(a) \( an equilateral triangle \)
(b) \( a right triangle \)
(c) \( an obtuse triangle \)
(d) \( an isosceles triangle always \)
Show Answer & Explanation

Answer: (b) \( a right triangle \)

Explanation:
1. Its sides are half of the original sides, so it is similar to the original triangle (the Pythagoras relation still holds).

Teacher's Note:
1. It is similar to the original.

Question 11: The figure formed by joining the mid-points of consecutive sides of a quadrilateral is a
(a) \( rectangle \)
(b) \( rhombus \)
(c) \( parallelogram \)
(d) \( trapezium that is not a parallelogram \)
Show Answer & Explanation

Answer: (c) \( parallelogram \)

Explanation:
1. Each side of the new figure is parallel to a diagonal and half its length; opposite sides are parallel and equal.

Teacher's Note:
1. Use the mid-point theorem in two triangles.

Question 12: In any quadrilateral, if a pair of opposite sides is equal, then it is
(a) always a parallelogram
(b) always a rhombus
(c) always a rectangle
(d) not necessarily a parallelogram
Show Answer & Explanation

Answer: (d) not necessarily a parallelogram

Explanation:
1. A trapezium with equal non-parallel sides (isosceles trapezium) has one pair of equal opposite sides but is not a parallelogram.

Teacher's Note:
1. Look for a counterexample.

Question 13: If all the angles of a quadrilateral are equal, then it is
(a) a rectangle, hence a parallelogram
(b) a rhombus that is not a rectangle
(c) a trapezium that is not a parallelogram
(d) a kite that is not a parallelogram
Show Answer & Explanation

Answer: (a) a rectangle, hence a parallelogram

Explanation:
1. Each angle is \( 90^\circ \), so opposite sides are parallel (co-interior angles add to \( 180^\circ \)) and the figure is a rectangle.

Teacher's Note:
1. Each angle is 90 degrees.

Question 14: If three sides of a quadrilateral are equal, then it
(a) must be a parallelogram
(b) need not be a parallelogram
(c) must be a rhombus
(d) must be a square
Show Answer & Explanation

Answer: (b) need not be a parallelogram

Explanation:
1. A kite can have three equal sides without being a parallelogram.

Teacher's Note:
1. Try a kite.

Question 15: If three angles of a quadrilateral are equal, then it
(a) must be a parallelogram
(b) must be a rectangle
(c) need not be a parallelogram
(d) must be a square
Show Answer & Explanation

Answer: (c) need not be a parallelogram

Explanation:
1. Angles \( 80^\circ,80^\circ,80^\circ,120^\circ \) add to 360 and the figure is not a parallelogram (opposite angles are unequal).

Teacher's Note:
1. Find angles that satisfy the sum but not the parallelogram test.

Question 16: If all the sides of a quadrilateral are equal, then it
(a) need not be a parallelogram
(b) is a rectangle
(c) is a trapezium only
(d) is a parallelogram (a rhombus)
Show Answer & Explanation

Answer: (d) is a parallelogram (a rhombus)

Explanation:
1. Both pairs of opposite sides are equal, so it is a parallelogram; it is a rhombus.

Teacher's Note:
1. Opposite sides equal means parallelogram.

Question 17: In parallelogram \( ABCD \), \( AB=10 \) cm and \( AD=6 \) cm. The bisector of \( \angle A \) meets \( DC \) at \( E \); \( AE \) and \( BC \) produced meet at \( F \). Then \( CF \) is
(a) \( 4 cm \)
(b) \( 6 cm \)
(c) \( 10 cm \)
(d) \( 2 cm \)
Show Answer & Explanation

Answer: (a) \( 4 cm \)

Explanation:
1. \( \angle BAF=\angle AFB \) (alternate angles with \( AB\parallel DC \) and the bisector), so \( BF=AB=10 \).
2. \( CF=BF-BC=10-6=4 \) cm.

Teacher's Note:
1. Triangle ABF is isosceles.

Question 18: The quadrilateral formed by joining the mid-points of the sides of a rectangle is a
(a) \( rectangle \)
(b) \( rhombus \)
(c) \( square \)
(d) \( trapezium \)
Show Answer & Explanation

Answer: (b) \( rhombus \)

Explanation:
1. Each side equals half a diagonal and the diagonals of a rectangle are equal, so all four sides are equal; it is a parallelogram with equal sides.

Teacher's Note:
1. Diagonals of a rectangle are equal.

Question 19: The quadrilateral formed by joining the mid-points of the sides of a square is a
(a) \( rhombus that is not a square \)
(b) \( rectangle that is not a square \)
(c) \( square \)
(d) \( parallelogram only \)
Show Answer & Explanation

Answer: (c) \( square \)

Explanation:
1. Sides are half the diagonals, which are equal and perpendicular, so the new figure has equal sides and right angles.

Teacher's Note:
1. Diagonals of a square are equal and perpendicular.

Question 20: In \( \triangle ABC \), \( P,Q,R \) are the mid-points of \( BC,CA,AB \); \( PR \) and \( BQ \) meet at \( X \), \( CR \) and \( PQ \) meet at \( Y \). If \( BC=20 \) cm, then \( XY \) is
(a) \( 10 cm \)
(b) \( 4 cm \)
(c) \( 2.5 cm \)
(d) \( 5 cm \)
Show Answer & Explanation

Answer: (d) \( 5 cm \)

Explanation:
1. \( BPQR \) is a parallelogram, so \( X \) is the mid-point of \( PQ \); similarly \( Y \) is the mid-point of \( PQ \) in the other parallelogram.
2. \( XY=\frac12RQ=\frac12\cdot\frac12BC=\frac14BC=5 \) cm.

Teacher's Note:
1. Apply the mid-point theorem twice.

Question 21: In trapezium \( ABCD \) with \( AB\parallel DC \), \( E,F \) are the mid-points of \( AD \) and \( BC \). If \( AB=8 \) cm and \( CD=14 \) cm, then \( EF \) is
(a) \( 11 cm \)
(b) \( 22 cm \)
(c) \( 6 cm \)
(d) \( 3 cm \)
Show Answer & Explanation

Answer: (a) \( 11 cm \)

Explanation:
1. \( EF\parallel AB \) and \( EF=\frac12(AB+CD)=\frac12(8+14)=11 \) cm.

Teacher's Note:
1. The line joining mid-points of the legs is half the sum of the parallel sides.

Question 22: The area of a rhombus with diagonals \( 16 \) cm and \( 12 \) cm is
(a) \( 192\text{ cm}^2 \)
(b) \( 96\text{ cm}^2 \)
(c) \( 48\text{ cm}^2 \)
(d) \( 28\text{ cm}^2 \)
Show Answer & Explanation

Answer: (b) \( 96\text{ cm}^2 \)

Explanation:
1. Area \( =\frac12\times16\times12=96 \) cm\( ^2 \).

Teacher's Note:
1. Half the product of the diagonals.

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FAQs

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