ML Aggarwal Solution Class 9 Chapter 13 Rectilinear Figures MCQs

 MCQs

Choose the correct answer from the given four options (1 to 12):

Question 1

Three angles of a quadrilateral are 75°, 90° and 75°. The fourth angle is

(a) 90°

(b) 95°

(c) 105°

(d) 120°

Sol :

Sum of 4 angles of a quadrilateral = 360° 

Sum of three angles = 75° + 90° + 75° = 240° 

Fourth angle = 360° – 240° = 120° 

Ans (d)


Question 2

A quadrilateral ABCD is a trapezium if

(a) AB = DC

(b) AD = BC

(c) ∠A + ∠C = 180°

(d) ∠B + ∠C = 180°

Sol :

A quadrilateral ABCD is a trapezium if ∠B + ∠C= 180°

(Sum of co-interior angles) (d)


Question 3

If PQRS is a parallelogram, then ∠Q – ∠S is equal to

(a) 90°

(b) 120°

(c) 0°

(d) 180°

Sol :

PQRS is a parallelogram ∠Q – ∠S = 0

(∵ Opposite angles of a parallelogram, are equal) (c)


Question 4

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is

(a) 55°

(b) 50°

(c) 40°

(d) 25°

Sol :

In a rectangle a diagonal is inclined to one side of the rectangle is 25°






i.e. ∠OAB=25°

But OA=OB

∴∠OBA=25°

But ext.∠COB=∠OAB+∠OBA

=25°+25°=50° 

Ans (c)


Question 5

ABCD is a rhombus such that ∠ACB = 40°. Then ∠ADB is

(a) 40°

(b) 45°

(c) 50°

(d) 60°

Sol :

In rhombus ABCD, ∠ACB = 40°







∴∠OBC=90°-40°=50°

and ∠ADO=∠OBC (alternate angles)

∴∠ADB=50°

Ans (c)


Question 6

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠D AC = 32° and ∠AOB = 70°, then ∠DBC is equal to

(a) 24°

(b) 86°

(c) 38°

(d) 32°

Sol :

Diagonals AC and BD of parallelogram ABCD intersecting each other at O






∠DAC=32° , ∠AOB=70°

∠ADO=70°-32° (ext.∠AOB=70°)

=38°

But ∠DBC=∠ADO or ∠ADB

∴∠DBC=38°

Ans (c)


Question 7

If the diagonals of a square ABCD intersect each other at O, then ∆OAB is

(a) an equilateral triangle

(b) a right angled but not an isosceles triangle

(c) an isosceles but not right angled triangle

(d) an isosceles right angled triangle

Sol :

Diagonals of square ABCD intersect each other at O

(∵Diagonals of a square bisect each other at right angles)

(∵∠AOB=90° and AO=BO)






⇒ΔOAB is an isosceles

Ans (d)


Question 8

If the diagonals of a quadrilateral PQRS bisect each other, then the quadrilateral PQRS must be a

(a) parallelogram

(b) rhombus

(c) rectangle

(d) square

Sol :

Diagonals of a quadrilateral PQRS bisect each other, then quadrilateral must be a parallelogram.

(∵ A rhombus, rectangle and square are also parallelogram) 

Ans (a)


Question 9

If the diagonals of a quadrilateral PQRS bisect each other at right angles, then the quadrilateral PQRS must be a

(a) parallelogram

(b) rectangle

(c) rhombus

(d) square

Sol :

Diagonals of quadrilateral PQRS bisect each other at right angles, then quadrilateral PQRS [ must be a rhombus.

(∵ Square is also a rhombus with each angle equal to 90°) 

Ans (c)


Question 10

Which of the following statement is true for a parallelogram?

(a) Its diagonals are equal.

(b) Its diagonals are perpendicular to each other.

(c) The diagonals divide the parallelogram into four congruent triangles.

(d) The diagonals bisect each other.

Sol :

For a parallelogram an the statement ‘The diagonals bisect each other’ is true.

Ans (d)


Question 11

Which of the following is not true for a parallelogram?

(a) opposite sides are equal

(b) opposite angles are equal

(c) opposite angles are bisected by the diagonals

(d) diagonals bisect each other

Sol :

The statement that in a parallelogram, .the opposite angles are bisected by the diagonals, is not true in each case.

Ans (c)


Question 12

A quadrilateral in which the diagonals are equal and bisect each other at right angles is a

(a) rectangle which is not a square

(b) rhombus which is not a square

(c) kite which is not a square

(d) square

Sol :

In a quadrilateral, if diagonals are equal and bisect each other at right angles, is a square. (d)

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