# Free Quadrilaterals 02 Practice Test - 9th Grade

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°.

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.

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.

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.

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. 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

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

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.

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.

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.