# Free Understanding Quadrilaterals 02 Practice Test - 8th Grade

### Question 1

Which of the following is/are concave quadrilaterals?

I & III

II & IV

IV

II

#### SOLUTION

Solution :C

A line segment connecting any two non-consecutive vertices of a polygon is known as diagonal.A polygon with an exterior diagonal is known as concave polygon.

Only in these two options, there exists an exterior diagonal. So, these are concave polygons. But II is a concave pentagon. Only IV is a concave quadrilateral. Moreover, a concave polygon has one or more interior angle greater than 180°.

### Question 2

Which of the following is not true for the figure below?

AC ⊥ BD

∠ADB = ∠ABD

∠DAB = ∠DCB

#### SOLUTION

Solution :D

It is given that AB = AD and BC = CD.

Since, two pairs of adjacent sides are equal, the ABCD is a kite.

According to the properties of a kite:

AC⊥BD

[Diagonals of kite are perpendicular.]

In ΔABD,

∠ADB = ∠ABD [∵BA=DA and angles opposite to equal sides are equal]

But, ∠DAB ≠ ∠DCB

### Question 3

Which of the following quadrilaterals has/have equal length of diagonals?

i) Rhombus

ii) Rectangle

iii) Square

iv) Kite

v) Parallelogram

i, ii, iii

ii, iii

ii, iii, v

ii, iii, iv

#### SOLUTION

Solution :B

Rhombus has unequal diagonals which are perpendicular bisectors.

Square has equal diagonals which are perpendicular bisectors.

Rectangle has equal diagonals which are perpendicular bisectors .

Kite has unequal diagonals in which the longer one bisects the other.

Parallelogram has unequal diagonals unless it is a square or a rectangle. The diagonals bisect each other.

### Question 4

Find ∠ABF from the given figure.

30∘

45∘

60∘

75∘

#### SOLUTION

Solution :C

∠BCD+∠BCH=180∘ [ Linear pair]

∠BCD = 180∘ - 35∘ = 145∘

In quadrilateral BEDC, ∠BED + ∠EDC + ∠DCB + ∠CBE = 360∘

∠CBE = 360∘ - (105∘ + 50∘ + 145∘) = 60∘

So, ∠ABF = ∠CBE = 60∘(Vertically opposite angles)

### Question 5

ABCD is a parallelogram in which ∠DCB and ∠ABC are in ratio 2:7. Find the sum of ∠ABD and ∠ADB.

40∘

50∘

70∘

140∘

#### SOLUTION

Solution :D

∠DCB+∠ABC=180∘

[Adjacent angles of a parallelogram are supplementary]

⇒2t+7t=180∘

[∵∠DCB and ∠ABC are in ratio 2:7]

⇒t=20∘

∴∠DCB=2t=2×20∘=40∘

and ∠ABC=7t=7×20∘=140∘

Now, ∠DAB=∠DCB=40∘

[Opposite angles of a parallelogram are equal]

∠DAB+∠ADB+∠ABD=180∘

[Sum of the angles of a triangle]

⇒40∘+∠ADB+∠ABD=180∘

⇒∠ADB+∠ABD=140∘

### Question 6

What is the measure of any exterior angle of a regular nonagon?

40∘

100∘

140∘

90∘

#### SOLUTION

Solution :A

Sum of the exterior angles of a polygon (irrespective of the number of sides) is 360∘.

In a nonagon, the measure of all exterior angles will be the same i.e. 360∘.

Also, nonagon has 9 sides.

So, measure of each exterior angle

= 360∘9=40∘

### Question 7

The total number of parallelograms in this figure is

#### SOLUTION

Solution :Rectangles are also parallelograms. They are shown in color "blue" in the below figures. Hence, there are 7 parallelograms in the figure.

### Question 8

Square is a regular quadrilateral.

True

#### SOLUTION

Solution :A

A polygon is called a regular polygon if it is equiangular and equilateral. i.e., All the angles are equal and measure of all the sides are equal.

Square is quadrilateral with all the angles equal to 90∘ and all the sides of equal length.

⟹ Square is a regular quadrilateral.

Hence, the given statement is true.

### Question 9

The diagonal of a parallelogram divides it into two congruent triangles.

True

False

#### SOLUTION

Solution :A

ΔABD and ΔCDB

AB = CD (Opposite sides of a parallelogram)

AD = CB (Opposite sides of a parallelogram)

BD = DB (Common)

So, ΔABD ≅ ΔCDB (By SSS congruence condition)

### Question 10

Select the correct statements.

All rhombuses are parallelograms

All kites are rhombuses

#### SOLUTION

Solution :A and C

Since, the opposite sides of a rhombus have the same length it is also a parallelogram. So, a rhombus has all the properties of a parallelogram and also that of a kite. A quadrilateral with exactly two pairs of equal consecutive sides is a kite. This condition is also satisfied by Rhombus. So, all rhombuses are kites but converse is always not true