# 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.