Free Quadrilaterals 02 Practice Test - 9th Grade 

Question 1

The sum of angles of a kite is:

A. 180
B. 360
C. 480
D. 90

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?

A.

Square

B.

Circle

C.

Rhombus

D.

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:

A.

Triangle

B.

Circle

C.

Parallelogram

D.

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.

A.

True

B.

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.

A.

True

B.

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).

A.

AFE=x

B.

FBD=x+y

C.

BCD=z

D.

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+zy
CDG=z

Question 7

The angles of a quadrilateral are in the ratio 1: 2 : 3 : 4. The angles of the quadrilateral are respectively ____.

A.

144, 108, 60, 48

B.

36, 72, 108, 144

C.

30, 60, 90, 120

D.

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.

A.

True

B.

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.

A.

True

B.

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.