# Free Understanding Quadrilaterals 03 Practice Test - 8th Grade

### Question 1

Which among the following has the most number of diagonals?

Triangle

Quadrilateral

Pentagon

Can't be determined

#### SOLUTION

Solution :C

The pentagon has the most number of vertices among the options. Hence, it has the most number of diagonals.

### Question 2

In the given diagram, the value of x is

#### SOLUTION

Solution :In quadrilateral ABCD,

∴∠ABC+∠BCD+∠CDA+∠DAB=360∘40∘+50∘+∠CDA+70∘=360∘⇒∠CDA+160∘=360∘⇒∠CDA=360∘−160∘=200∘

Now, ∠CDA+∠ADC=360∘ (∵ Angle at a point)

200∘+x=360∘⇒x=360∘−200∘⇒x=160∘

### Question 3

In a concave polygon, no part of any of their diagonals is external.

True

False

#### SOLUTION

Solution :B

A concave polygon will have some part of at least one diagonal external.

### Question 4

Which of the following are definitely regular polygons?

Triangle

Square

Rhombus

Rectangle

#### SOLUTION

Solution :B

A regular polygon is a polygon which is equiangular i.e. all the angles are equal and equilateral i.e. all the sides are equal.

The triangle if equilateral is a regular polygon. If not, it is not a regular polygon.

A rhombus has equal sides but not equal angles.

A Rectangle has equal angles but not equal sides. Hence, they are not regular polygons.

A square has equal sides and equal angles. Hence, it is a regular polygon.

### Question 5

Which of the following is true?

All squares are rectangles

All rectangles are squares

All rectangles are rhombuses

#### SOLUTION

Solution :A

The statement that all squares are rectangles is true because a square is a special type of rectangle where, the adjacent sides are equal.

### Question 6

If ABCD is a parallelogram, then the angle bisectors of ∠A and ∠D meet at ‘O’. The measure of ∠AOD is 45∘

True

False

#### SOLUTION

Solution :B

Let∠A=x∘

then ∠D=(180−x)∘

(Since the adjacent angles of a parallelogram sum up to 180∘)

∴∠A2=x2=∠DAO

and∠D2=(180−x)2=90−x2=∠ADO

In ΔAOD,

∠AOD+∠ADO+∠DAO=180∘ [Angle sum property of a triangle]

∠AOD=180∘−[∠ADO+∠DAO]

∠AOD=180∘−[x2+90−x2]

or ∠AOD=180−90=90∘

∴ The measure of ∠AOD is 90∘

### Question 7

Which of the following is not a model for a plane surface?

Top surface of table

Surface of paper

Body of car

None of these

#### SOLUTION

Solution :C

The body of a car is a 3 dimensional surface. It is not a plane 2 dimensional surface

### Question 8

A quadrilateral with two distinct pairs of equal-length adjacent sides is known as

#### SOLUTION

Solution :D

A quadrilateral with two distinct pairs of equal-length adjacent sides is known as a kite.

### Question 9

Two sides of a kite have lengths 7.8 cm and 11 cm. Then the perimeter of the kite is

#### SOLUTION

Solution :C

Let ‘a’ be one side of the kite = 7.8 cm

and‘b’ be the other side of the kite = 11 cm

Perimeter of the kite = 2a + 2b units

=2×7.8+2×11=15.6+22=37.6 cm

### Question 10

Which of the following is true?

All parallelograms are kites

All kites are parallelograms

Some kites are parallelograms

#### SOLUTION

Solution :C

The kites that have all the sides equal and two pairs of sides parallel are parallelograms. These kites are rhombuses.

Hence, some kites are parallelograms.