Quadrilaterals CBSE Questions & Answers

Quadrilaterals

This is Mathematics Class 09 Quadrilaterals CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The angle between two altitudes of a Parallelogram through the vertex of an obtuse angle of the Parallelogram of \(60^\circ \). Find the angles of the Parallelogram
  • A
    150 \(^\circ \), 150 \(^\circ \), 30 \(^\circ \), 30 \(^\circ \)
  • B
    120 \(^\circ \), 60 \(^\circ \), 120 \(^\circ \), 60 \(^\circ \)
    Correct
  • C
    200 \(^\circ \), 100 \(^\circ \), 30 \(^\circ \), 30 \(^\circ \)
  • D
    110 \(^\circ \), 50 \(^\circ \), 105 \(^\circ \), 105 \(^\circ \)
2
ABCD is a Trapezium in which AB\(\parallel \)DC and \(\angle A = \angle B = 45^\circ \). Find angles C and D of the Trapezium
  • A
    120 \(^\circ \), 120 \(^\circ \)
  • B
    135 \(^\circ \), 135 \(^\circ \)
    Correct
  • C
    200 \(^\circ \), 50 \(^\circ \)
  • D
    150 \(^\circ \), 150 \(^\circ \)
3
One Angle of a quadrilateral is of 108 \(^\circ \) and the remaining three angles are equal. Find each of the three equal angles.
  • A
    90 \(^\circ \), 90 \(^\circ \), 84 \(^\circ \)
  • B
    84 \(^\circ \), 84 \(^\circ \), 84 \(^\circ \)
    Correct
  • C
    84 \(^\circ \), 90 \(^\circ \), 90 \(^\circ \)
  • D
    90 \(^\circ \), 84 \(^\circ \), 90 \(^\circ \)
4
Angles of a quadrilateral are in the ratio 3 : 4 : 4 : 7. Find all the angles of the quadrilateral.
  • A
    60 \(^\circ \), 120 \(^\circ \), 80 \(^\circ \), 140 \(^\circ \)
  • B
    70 \(^\circ \), 70 \(^\circ \), 100 \(^\circ \), 100 \(^\circ \)
  • C
    60 \(^\circ \), 80 \(^\circ \), 100 \(^\circ \), 90 \(^\circ \)
  • D
    60 \(^\circ \), 80 \(^\circ \), 80 \(^\circ \), 140 \(^\circ \)
    Correct
5
The angles of the quadrilateral are in the ratios 3 : 5 : 9 : 13. Find all the angles of the Quadrilateral
  • A
    40 \(^\circ \), 50 \(^\circ \), 80 \(^\circ \), 150 \(^\circ \)
  • B
    100 \(^\circ \), 60 \(^\circ \), 36 \(^\circ \), 156 \(^\circ \)
  • C
    36 \(^\circ \), 60 \(^\circ \), 108 \(^\circ \), 156 \(^\circ \)
    Correct
  • D
    36 \(^\circ \), 60 \(^\circ \), 108 \(^\circ \), 154 \(^\circ \)
6
P, Q, R are the mid- points of AB, BC, AC res, If AB = 10cm, BC = 8cm, AC = 12cm, Find the perimeter of \(\triangle \)PQR.
Question 6 figure 1
  • A
    15.5cm
  • B
    14cm
  • C
    13cm
  • D
    15cm
    Correct
7
The Diagonals AC and BD of a Parallelogram ABCD intersect each other at the point O such that \(\angle DAC = 30^\circ \) and \(\angle AOB = 70^\circ \). Then, \(\angle DBC\)?
  • A
    30 \(^\circ \)
  • B
    45 \(^\circ \)
  • C
    35 \(^\circ \)
  • D
    40 \(^\circ \)
    Correct
8
In the given figure, ABCD is a Rhombus. Then,
Question 8 figure 1
  • A
    \(({\text{A}}{{\text{C}}^{\text{2}}} + {\text{ B}}{{\text{D}}^{{\text{2}})}} = {\text{ 3A}}{{\text{B}}^{\text{2}}}\)
  • B
    \({\text{A}}{{\text{C}}^{\text{2}}} + {\text{ B}}{{\text{D}}^{\text{2}}} = {\text{ A}}{{\text{B}}^{\text{2}}}\)
  • C
    \({\text{A}}{{\text{C}}^{\text{2}}} + {\text{ B}}{{\text{D}}^{\text{2}}} = {\text{ 4A}}{{\text{B}}^{\text{2}}}\)
    Correct
  • D
    \({\text{A}}{{\text{C}}^{\text{2}}} + {\text{ B}}{{\text{D}}^{\text{2}}} = {\text{ 2A}}{{\text{B}}^{\text{2}}}\)
9
In a Trapezium ABCD, if AB \(\parallel \) CD, then \(\left( {{\text{A}}{{\text{C}}^{\text{2}}} + {\text{ B}}{{\text{D}}^{\text{2}}}} \right)\)= ?
Question 9 figure 1
  • A
    \({\text{B}}{{\text{C}}^{\text{2}}} + {\text{ A}}{{\text{D}}^{\text{2}}} + {\text{ 2AB}}.{\text{CD}}\)
    Correct
  • B
    \({\text{A}}{{\text{B}}^{\text{2}}} + {\text{ C}}{{\text{D}}^{\text{2}}} + {\text{ 2AD}}.{\text{BC}}\)
  • C
    \({\text{B}}{{\text{C}}^{\text{2}}} + {\text{ A}}{{\text{D}}^{\text{2}}} + {\text{ 2BC}}.{\text{AD}}\)
  • D
    \({\text{A}}{{\text{B}}^{\text{2}}} + {\text{ C}}{{\text{D}}^{\text{2}}} + {\text{ 2AB}}.{\text{CD}}\)
10
In the Given Figure, ABCD is a Parallelogram, M is the mid-point of BD and BD bisects \(\angle B\) as well as \(\angle D\). Then, \(\angle AMB\)?
Question 10 figure 1
  • A
    90 \(^\circ \)
    Correct
  • B
    80 \(^\circ \)
  • C
    10 \(^\circ \)
  • D
    100 \(^\circ \)
11
In a Trapezium ABCD, if E and F be the mid-points of the Diagonals AC and BD res. Then EF =?
Question 11 figure 1
  • A
    \(\frac{1}{2}\)CD
  • B
    \(\frac{1}{2}\)AB
  • C
    \(\frac{1}{2}\)(AB – CD)
    Correct
  • D
    \(\frac{1}{2}\) (AB + CD)
12
In the given figure, ABCD is a Parallelogram and E is the mid-point of BC. Also, DE and AB when produced meet at F. Then
Question 12 figure 1
  • A
    \({\text{A}}{{\text{F}}^{\text{2}}} = {\text{ 2 A}}{{\text{B}}^{\text{2}}}\)
  • B
    AF = 2AB
    Correct
  • C
    AF = 3/2 AB
  • D
    AF = 3AB
13
In the given figure, ABCD is a Parallelogram in which \(\angle BDC = 45^\circ \) and \(\angle BAD = 75^\circ \). Then. \(\angle CBD\) = ?
  • A
    60 \(^\circ \)
    Correct
  • B
    50 \(^\circ \)
  • C
    65 \(^\circ \)
  • D
    75 \(^\circ \)
14
In the adjoining figure, ABCD is a square. A line segment CX cuts at X and the diagonal BD at O such that \(\angle COD = 80^\circ \) and \(\angle OXA = x^\circ \). Find the value of X?
  • A
    125.0
    Correct
  • B
    24
  • C
    127
  • D
    23
15
ABCD is a Rhombus. Then, find the value of x and y?
  • A
    45 and 45
  • B
    37 and 37
  • C
    35 and 35
    Correct
  • D
    40 and 40