Free Quadrilaterals 02 Practice Test - 9th Grade
Question 1
The sum of angles of a kite is:
SOLUTION
Solution : B
A kite is a quadrilateral.
We know that, the sum of the angles of a quadrilateral is equal to 360°.
⇒ The sum of the angles of a kite is also equal to 360°.
Question 2
Which of the following is not a quadrilateral?
Square
Circle
Rhombus
Trapezium
SOLUTION
Solution : B
A quadrilateral is a polygon with four sides and four vertices.
A quadrilateral has four sides, four angles and four vertices. Square, trapezium and rhombus are quadrilaterals. A circle can be approximated as a polygon with infinite sides but it is not a polygon.
It is because a polygon must have straight edges (sides). A circle doesn't have straight sides.
Question 3
If both pairs of opposite sides of a quadrilateral are parallel, then it is called:
Triangle
Circle
Parallelogram
All of these
SOLUTION
Solution : C
A parallelogram is a quadrilateral whose both pairs of opposite sides are parallel.
Question 4
The fundamental difference between a rhombus and a kite is that the sum of adjacent angles are supplementary in a kite.
True
False
SOLUTION
Solution : B
A rhombus can be considered as a parallelogram with all sides equal. Hence its adjacent angles are supplementary, whereas a kite does not have any sides parallel and thus its adjacent angles need not be supplementary.
Question 5
The three angles of a quadrilateral are 75∘, 90∘ and 75∘. The quadrilateral can be a parallelogram.
True
False
SOLUTION
Solution : B
Sum of all angles of a quadrilateral is 360∘.
Fourth angle=360∘−(75∘+90∘+75∘)=120∘
Since the pairs of opposite angles of a parallelogram are equal, this quadrilateral cannot be a parallelogram since it has three different angles and only one pair of equal angles.
Question 6
In the above figure, ACDF, ABEF and BCDE are parallelograms. Analyse the given figure and choose the correct option(s).
∠AFE=x
∠FBD=x+y
∠BCD=z
∠CDG=x+y
SOLUTION
Solution : B and C
Since ABEF is a parallelogram, so AF || BE and BF is the transversal.
∴∠AFB=∠FBE=x
[Alternate angles]
Also, since BCED is a parallelogram,
BE || CD and BD is the transversal.
∴∠CDB=∠EDB=y
[Alternate angles]
Now,
∠FBD=∠FBE+∠EBD
∠FBD=x+y
And,
∠AFE=∠BED
[Corresponding angles]
∴∠AFE=z
∠BED=∠BCD=z
[opposite angles of a parallelogram]
∠CDG+∠BCD=∠EBD+∠BED
[Sum of opposite interior angles is equal to exterior angle of a triangle]
⇒∠CDG=y+z−y
⇒∠CDG=z
Question 7
The angles of a quadrilateral are in the ratio 1: 2 : 3 : 4. The angles of the quadrilateral are respectively ____.
144∘, 108∘, 60∘, 48∘
36∘, 72∘, 108∘, 144∘
30∘, 60∘, 90∘, 120∘
10∘, 20∘, 30∘, 40∘
SOLUTION
Solution : B
Let the smallest angle of quadrilateral be x∘.
Then, the angles of the quadrilateral will be x∘, 2x∘, 3x∘ and 4x∘.
Sum of the angles of a quadrilateral is 360∘.
⇒360∘=x+2x+3x+4x
⇒10x=360∘
∴x=36∘,2x=72∘,3x=108∘ and 4x=144∘
Question 8
The quadrilateral formed by joining the mid points of the sides of a quadrilateral, in order, is a
SOLUTION
Solution :By joining the mid points of the sides of a quadrilateral, another quadrilateral is formed whose opposite sides will be equal and parallel. Hence the quadrilateral formed is a parallelogram.
Question 9
Square, rectangle and rhombus are all parallelograms.
True
False
SOLUTION
Solution : A
A parallelogram is a quadrilateral whose both pairs of opposite sides are equal and parallel. Since the pairs of opposite sides equal and parallel in a square, rhombus and rectangle, they are all parallelograms.
Question 10
A trapezium is a parallelogram.
True
False
SOLUTION
Solution : B
In a trapezium only one pair of opposite sides are parallel.
In a parallelogram, both pairs of opposite sides are equal and parallel.
Therefore a trapezium is not a parallelogram.