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Quadrilaterals Maths - Quadrilaterals

Maharashtra Board - STD 9 - Maths (MSBSHSE - English Medium). 114 questions in this chapter.

Question types

Quadrilaterals question types

114 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

114
Questions
5
Question groups
5
Question types
Sample Questions

Quadrilaterals questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1MCQ(1M)1 Mark
Three statements are given below:
    $ (i)$ In a rectangle $\text{ABCD},$ the diagonal $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$
     $(ii)$ In a square $\text{ABCD},$ the diagonal $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$
     $(iii)$ In a rhombus $\text{ABCD},$ the diagonal $AC$ bisects $\angle\text{A}$ as well as $\angle\text{C}.$ Which is true?
  • A
    $I$ only
  • ✓
    $II$ and $III$
  • C
    $I$ and $III$
  • D
    $I$ and $II$

Answer: B.

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Q 2MCQ(1M)1 Mark
The figure formed by joining the mid $-$ points of the adjacent sides of a rhombus is a:
  • A
    Rhombus.
  • B
    Square.
  • ✓
    Rectangle.
  • D
    Parallelogram.

Answer: C.

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Q 3MCQ(1M)1 Mark
In the given figure $, \text{ABCD}$ is a parallelogram in which $\angle\text{BDC}=45^{\circ}$ and $\angle\text{BAD}=75^{\circ}.$ Then, $\angle\text{CBD}=?$
  • A
    $45^\circ$
  • B
    $55^\circ$
  • ✓
    $60^\circ$
  • D
    $75^\circ$

Answer: C.

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Q 5MCQ(1M)1 Mark
Three statements are given below:
        $(i)$ In $a \| gm$, the angle bisectors of two adjacent angles enclose a right angle.
        $(ii)$ The angle bisectors of $a \| gm$ form a rectangle.
        $(iii)$ The triangle formed by joining the mid $-$ points of the sides of an isosceles triangle is not                           necessarily an isosceles triangle. Which is true?
  • A
    $I$ only
  • B
    $II$ only
  • ✓
    $I$ and $II$
  • D
    $II$ and $III$

Answer: C.

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Q 82 Mark Question2 Marks
In the adjoining figure, ABCD is a trapezium in which AB || DC. If $\angle\text{A}=55^{\circ}$ and $\angle\text{B}=70^{\circ},$ find $\angle\text{C}$ and $\angle\text{D}.$
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Q 92 Mark Question2 Marks
In a parallelogram ABCD, points M and N have been taken on opposite sides AB and CD respectively such that AM = CN. Show that AC and MN bisect each other.
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Q 113 Mark Question3 Marks
M and N are points on opposite sides AD and BC of a parallelogram ABCD such that MN passes through the point of intersection O of its diagonals AC and BD. Show that MN is bisected at O.
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Q 123 Mark Question3 Marks
In the adjoining figure, M is the midpoint of side BC of a parallelogram ABCD such that $\angle\text{BAM}=\angle\text{DAM}.$ Prove that AD = 2CD.
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Q 144 Mark Question4 Marks
In the adjoining figure, ABCD is a parallelogram and E is the midpoint of side BC. If DEand AB when produced meet at F, prove that AF = 2AB.
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Q 164 Mark Question4 Marks
In the adjoining figure, ABCD is a parallelogram whose diagonals intersect each other at O. A line segment EOF is drawn to meet AB at E and DC at F. Prove that OE = OF.
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Q 184 Mark Question4 Marks
P , Q, R and S are respectively the midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD. Show that:
  1. PQ || AC and $\text{PQ}=\frac{1}{2}\text{AC}$
  2. PQ || SR
  3. PQRS is a parallelogram.
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Q 195 Mark Question5 Marks
In the adjoining figure, ABCD is a parallelogram in which $\angle\text{DAB}=80^{\circ}$ and $\angle\text{DBC}=60^{\circ}.$ Calculate $\angle\text{CDB}$ and $\angle\text{ADB}.$
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Q 215 Mark Question5 Marks
In the adjoining figure, ABCD is a square. A line segment CX cuts AB at X and the diagonal BD at O such that $\angle\text{COD}=80^{\circ}$ and $\angle\text{OXA}=\text{x}^{\circ}.$ Find the value of x.
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