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Quadrilaterals MATHS - Quadrilaterals

Rajasthan Board (RBSE) - STD 9 - MATHS (Rajasthan - English Medium). 358 questions in this chapter.

Question types

Quadrilaterals question types

358 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

358
Questions
8
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 1M.C.Q1 Mark
The Quadrilateral forms by joining the mid-points of the sides of a Quadrilateral PQRS, taken in order, is a Rhombus if:
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Q 2M.C.Q1 Mark
Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is:
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Q 4M.C.Q1 Mark
If $\angle\text{A},\ \angle\text{B},\ \angle\text{C}$ and $\angle\text{D}$ of a quadrilateral ABCD, taken in order, are in the ratio 3 : 7 : 6 : 4 then ABCD is a:
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Q 5M.C.Q1 Mark
If an angle of a parallelogram is two-third of its adjacent angle, the smallest angle of the parallelogram is:
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Q 6Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A parallelogram consists of two congruent triangles.
Reason: Diagonal of a parallelogram divides it into two congruent triangles.
  1. Both assertion and reason are true and reason is the correct enatixplaon of assertion.
  2. Both assertion and reason are true but reason is not the correct explanation of assertion.
  3. Assertion is true but reason is false.
  4. Assertion is false but reason is true.
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Q 7Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A parallelogram consists of two congruent triangles.
Reason: Diagonal of a parallelogram divides it into two congruent triangles.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
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Q 8Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: ABCD is a square. AC and BD intersect at O. The measure of $\angle\text{ABC}=900.$
Reason: Diagonals of a square bisect each other at right angles.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
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Q 9Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: A rectangle is 12cm wide, and 5cm tall, 13cm is the length of a diagonal.
Reason: A rectangle is 12cm wide, and 5cm tall, 13cm is the length of a diagonal.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
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Q 10Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Every square is a rectangle.
Reason: Because it is a quadrilateral with all four angles right angles.
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
  2. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
  3. Assertion is true but the reason is false.
  4. Both assertion and reason are false.
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Q 232 Marks Questions2 Marks
l, m and n are three parallel lines intersected by transversal p and q such that l, m and n cut-off equal intercepts AB and BC on p Show that l, m and n cut-off equal intercepts DE and EF on q also.

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Q 242 Marks Questions2 Marks
In $\triangle ABC$, D, E and F are respectively the mid-points of sides AB, BC and CA. Show that $\triangle ABC$ is divided into four congruent triangles by joining D, E and F.
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Q 293 Marks Question3 Marks
In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

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Q 303 Marks Question3 Marks
ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F. Show that F is the mid-point of BC.
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Q 355 Marks Questions5 Marks
$\text{ABC}$ is a triangle right angled at $C.$ A line through the mid$-$point $M$ of hypotenuse $AB $ and parallels to $BC$ intersects $AC$ at $D$ Show that :
  1. $D$ is the mid$-$point of $AC$
  2. $MD \perp AC$
  3. $CM = MA =  \frac{1}{2} AB$
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Q 36Case study (4 Marks)4 Marks
Read the Source/ Text given below and answer any four questions:
Chocolate is in the form of a quadrilateral with sides $6\ cm$ and $10\ cm, 5\ cm$ and$ 5\ cm ($as shown in the figure$)$ is cut into two parts on one of its diagonal by a lady. Part-I is given to her maid and part II is equally divided among a driver and gardener.
  1. Length of $BD:$
  1. $9\ cm$
  2. $8\ cm$
  3. $7\ cm$
  4. $6\ cm$
  1. Area of $\triangle\text{ABC}:$
  1. $24\ cm^2$
  2. $12\ cm^2$
  3. $42\ cm^2$
  4. $21\ cm^2$
  1. The sum of all the angles of a quadrilateral is equal to:
  1. $180^\circ$
  2. $270^\circ$
  3. $360^\circ$
  4. $90^\circ$
  1. A diagonal of a parallelogram divides it into two congruent:
  1. Square.
  2. Parallelogram.
  3. Triangles.
  4. Rectangle.
  1. Each angle of the rectangle is:
  1. More than $90^\circ$
  2. Less than $90^\circ$
  3. Equal to $90^\circ$
  4. Equal to $45^\circ$
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Q 37Case study (4 Marks)4 Marks
Read the Source/ Text given below and answer these questions:

Sohan wants to show gratitude towards his teacher by giving her a card made by him. He has three pieces of trapezium pasted one above the other as shown in fig. These pieces are arranged in a way that AB || HC || GD || FE. Also BC = CD = DE and AH = HG = GF = 6cm. He wants to decorate the card by putting up a colored tape on the nonparallel sides of the trapezium.
  1. Find the total length of colored tape required if DE = 4cm.
  1. 20cm
  2. 30cm
  3. 40cm
  4. 50cm
  1. ABHC is a trapezium in which AB || HC and $\angle\text{A}=\angle\text{B}=45^\circ.$ Find angles C and H of the trapezium.
  1. 135, 130
  2. 130, 135
  3. 135, 135
  4. 130, 130
  1. What is the difference between trapezium and parallelogram?
  1. Trapezium has 2 sides, and parallelogram has 4 sides.
  2. Trapezium has 4 sides, and parallelogram has 2 sides.
  3. Trapezium has 1 pair of parallel sides, and parallelogram has 2 pairs of parallel sides.
  4. Trapezium has 2 pairs of parallel sides, and parallelogram has 1 pair of parallel sides.
  1. Diagonals in isosceles trapezoid are ________.
  1. parallel.
  2. opposite.
  3. vertical.
  4. equal.
  1. ABCD is a trapezium where AB || DC, BD is the diagonal and E is the midpoint of AD. A line is drawn through E parallel to AB intersecting BC at F. Which of these is true?
  1. BF = FC
  2. EA = FB
  3. CF = DE
  4. None of these
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Q 38Case study (4 Marks)4 Marks
Read the Source/ Text given below and answer these questions:

There is a Diwali celebration in the DPS school Janakpuri New Delhi. Girls are asked to prepare Rangoli in a triangular shape. They made a rangoli in the shape of triangle ABC. Dimensions of $\triangle\text{ABC}$ are 26cm, 28cm, 25cm.
  1. In fig, R is mid-point of AB and RQ || BC then AQ is equal to:
  1. BC
  2. RB
  3. QC
  4. AD
  1. In fig R and Q are mid-points of AB and AC respectively. The length of RQ is:
  1. 14
  2. 13
  3. 12.5
  4. 13.5
  1. If Garland is to be placed along the side of $\triangle\text{QPR}$ which is formed by joining midpoint, what is the length of garland:
  1. 79cm
  2. 39.5cm
  3. 35cm
  4. 79.5cm
  1. In the following figure R, P and Q are the mid-points of AB, BC, and AC respectively. Which of the following is the area of $\triangle\text{PQR}?$
  1. $\frac12\text{ar (ABC)}$
  2. $\frac{1}{3}\text{ar (ABC)}$
  3. $\frac14\text{ar (ABC)}$
  4. $\frac16\text{ar (ABC)}$
  1. R, P, Q are the mid-points of corresponding sides AB, BC, CA in $\triangle\text{ABC}$ the figure so obtained BPQR will be:
  1. Parallelogram.
  2. Trapezium.
  3. Quadrilateral.
  4. None of these.
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Q 39Case study (4 Marks)4 Marks
Read the Source/ Text given below and answer these questions: A class teacher gave students coloured paper in the shape of a quadrilateral. She asks him to make a parallelogram from it using paper folding.

  1. One angle of a quadrilateral is 108° and the remaining three angles are equal, then each of the three equal angles:
  1. 90°
  2. 74°
  3. 84°
  4. 72°
  1. How can a parallelogram be formed by using paper folding?
  1. By finding diagonals of the quadrilateral.
  2. By joining mid pts. of sides of a quadrilateral.
  3. By finding angle bisectors.
  4. None of these.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if:
  1. PQRS is a rectangle.
  2. PQRS is a parallelogram.
  3. diagonals of PQRS are perpendicular.
  4. diagonals of PQRS are equal.
  1. In the figure, ABCD and AEFG are two parallelograms. If $\angle\text{C}=60^\circ,$ then $\angle\text{F}$ is:
  1. 30°
  2. 60°
  3. 90°
  4. 120°
  1. Which of the following is not true for a parallelogram?
  1. Opposite sides are equal.
  2. Opposite angles are equal.
  3. Opposite angles are bisected by the diagonals.
  4. Diagonals bisect each other.
  1. The angles of the quadrilateral are in the ratio 2 : 5 : 4 : 1? Which of the following is true?
  1. The largest angle in the quadrilateral is 150°.
  2. The smallest angle is 30°.
  3. The second-largest angle in the quadrilateral is 80°.
  4. Both the largest angle in the quadrilateral is 150° and The smallest angle is 30°.
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Q 40Case study (4 Marks)4 Marks
Read the Source/ Text given below and answer any four questions: During Maths Lab Activity each student was given four broomsticks of lengths 8cm, 8cm, 5cm, 5cm to make different types of quadrilaterals.

Using the above information answer the following questions:
  1. How many quadrilaterals can be formed using these sticks?
  1. Only One type of quadrilaterals can be formed.
  2. Two types of quadrilaterals can be formed.
  3. Three types of quadrilaterals can be formed.
  4. Four types of quadrilaterals can be formed.
  1. Name the types of quadrilaterals formed:
  1. Rectangle, parallelogram, kite.
  2. Rectangle, parallelogram, Trapizum.
  3. Rectangle, parallelogram, Square.
  4. Rectangle, Square, kite.
  1. In a trapezium ABCD, DC || AB and $\angle\text{A}=\angle\text{B}=45^\circ,$ the teacher asked the student to find $\angle\text{D}.$ Naresh answered it is ________.
  1. 105°
  2. 108°
  3. 135°
  4. 125°
  1. While discussing the properties of a parallelogram teacher asked about the relation between two angles x and y of a parallelogram as shown in fig. The teacher gave them 4 options as (if BC < CD):
  1. x > y
  2. x < y
  3. x = y
  4. None of these.
  1. P, Q, R, and S are respectively the mid-points of sides AB, BC, CD, and DA of quadrilateral ABCD in which AC = BD and $\text{AC}\bot\text{BD}, \text{PQRS},$ is a:
  1. Square.
  2. Rhombus.
  3. Kite.
  4. Parallelogram.
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