Quadrilaterals(9th Grade > Mathematics ) Questions and answers for exam Preparation

9th Grade > Mathematics

QUADRILATERALS MCQs

Total Questions : 57 | Page 3 of 6 pages

Question 21. The fundamental difference between a rhombus and a kite is that the sum of adjacent angles are supplementary in a kite.

True
False
Parallelogram
All of these

Discuss Question

Answer: Option B. -> False
:
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 22. Quadrilateral in which only one pair of opposite sides is parallel is known as__

Discuss Question

:
Trapezium is a quadrilateralin which only one pair of opposite sides is parallel.

Question 23. Which of the following is a regular quadrilateral?

Parallelogram
Square
Trapezium
Kite

Discuss Question

Answer: Option B. -> Square
:
B
A regular quadrilateral is a shape that has four equal sideswith all the interior angles equal.
Among the given options, only square has all its four sides equal with each angle being

90^{\circ}

Question 24. The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.

40∘, 100∘, 80∘, 140∘
60∘, 80∘, 100∘, 120∘
30∘, 40∘, 50∘, 60∘
10∘, 20∘, 30∘, 40∘

Discuss Question

Answer: Option B. -> 60∘, 80∘, 100∘, 120∘
:
B
The angles of a quadrilateral are in the ratio3:4:5:6.
Let the angles of the quadrilateralbe

3 x, 4 x, 5 x, 6 x

.
The sum of the angles of aquadrilateral is

360^{\circ}

\Rightarrow 3 x + 4 x + 5 x + 6 x = 360^{\circ}

\Rightarrow 18 x = 360^{\circ}

\Rightarrow x = 20^{\circ}

∴ 3 x = 60^{\circ}, 4 x = 80^{\circ}, 5 x = 100^{\circ}, 6 x = 120^{\circ}

Question 25. A diagonal of a parallelogram divides it into two congruent triangles.

True
False
Three angles are known.
Length of sides should be known

Discuss Question

Answer: Option A. -> True
:
A

A Diagonal Of A Parallelogram Divides It Into Two Congruent ...

Suppose ABCD is a parallelogram and BD is the diagonal.
There are two triangles -

Δ

ABD and

Δ

CDB
In

Δ

ABD and

Δ

CDB,
AD = BC (opposite sides of a parallelogram are equal)
AB = CD (opposite sides of a parallelogram are equal)
BD is common

∴

By SSS criterion of congruency,

Δ

ABD

≅

Δ

CDB
Hence, the given statement is true.

Question 26. A parallelogram whose all sides are equal is called a _____.

trapezium
rhombus
rectangle
kite

Discuss Question

Answer: Option B. -> rhombus
:
B

Trapezium cannot be a parallelogram.

Rhombus is a parallelogram, whose sides are always equal.

Rectangle is a parallelogram whose opposite sides are equal.

Kite is not a parallelogram.

A parallelogram whose all sides are equal is called a rhombus.

Question 27. Area of parallelogram is the product of base and corresponding height.

True
False
Three angles are known.
Length of sides should be known

Discuss Question

Answer: Option A. -> True
:
A
A parallelogram is made up of two triangles, each having an area equal to the halfof the product of base and corresponding height. Adding these two, we find the given statement to be true.

Question 28.

Which of the following is not a quadrilateral?

Square
Circle
Rhombus
Trapezium

Discuss Question

Answer: Option B. -> Circle
:
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 29.

The sum of angles of a kite is:

$180^{\circ}$
$360^{\circ}$
$480^{\circ}$
$90^{\circ}$

Discuss Question

Answer: Option B. ->

360^{\circ}

:
B

A kite is a quadrilateral.
We know that, the sum of the angles of a quadrilateral is equal to 360°.
$\Rightarrow$ The sum of the angles of a kite is also equal to 360°.

Question 30.

The three angles of a quadrilateral are $75^{\circ}$ , $90^{\circ}$ and $75^{\circ}$ . The quadrilateral can be a parallelogram.

True
False
Parallelogram
All of these

Discuss Question

Answer: Option B. -> False
:
B

Sum of all angles of a quadrilateral is $360^{\circ}$ .

$F o u r t h a n g l e = 360^{\circ} - (75^{\circ} + 90^{\circ} + 75^{\circ}) = 120^{\circ}$

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.