Quadrilaterals Test

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Quadrilaterals Test - 20

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Weekly Quiz Competition

Question 1
1 / -0

A parallelogram is a quadrilateral whose ...................... sides are parallel.

A
adjacent

B
congruent

C
opposite

D
linear

Solution

A parallelogram is a quadrilateral which has $$4$$ sides whose opposite sides are equal and parallel. It has $$2$$ pairs of parallel and equal sides.
Therefore, C is the correct answer.
Question 2
1 / -0

A parallelogram each of whose angle measures $$90^\circ$$ is

A
Rectangle

B
Rhombus

C
Triangle

D
Trapezium

Solution

In a parallelogram,
Both the pair of opposite sides are of equal length.
Opposite angles are equal and two adjacent angles are supplementary.
A rectangle is a parallelogram, in which each angle measures $$90^{o}$$.
Hence, a parallelogram each of whose angle measures $$90^{o}$$ is a rectangle.
Question 3
1 / -0

A quadrilateral whose all sides are equal and has four right angles is called a ____ .

A
rectangle

B
rhombus

C
kite

D
square

Solution

A figure with all sides equal and angles also equal is a square.
Therefore, option D is the correct answer.

Question 4

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Match the following.

$$(1)$$ Rectangle	(p) A quadrilateral having its opposite sides equal and parallel.
$$(2)$$ Square	(q) A parallelogram having its opposite sides equal and each of the angle is a right angle.
$$(3)$$ Parallelogram	(r) A parallelogram having all sides equal and each of the angle is a right angle.
$$(4)$$ Rhombus	(s) A quadrilateral in which a pair of opposite sides are parallel.
$$(5)$$ Trapezium	(t) A parallelogram having all sides equal.

$$1\rightarrow (t), 2\rightarrow (s), 3\rightarrow (r), 4\rightarrow (p), 5\rightarrow (q)$$

$$1\rightarrow (p), 2\rightarrow (q), 3\rightarrow (r), 4\rightarrow (s), 5\rightarrow (t)$$

$$1\rightarrow (r), 2\rightarrow (q), 3\rightarrow (t), 4\rightarrow (p), 5\rightarrow (s)$$

$$1\rightarrow (q), 2\rightarrow (r), 3\rightarrow (p), 4\rightarrow (t), 5\rightarrow (s)$$

Solution

1. Rectangle is a parallelogram with opposite sides equal and all sides at right angle to each other. Hence (q) is correct.

2. Square is a parallelogram with all sides equal and all the sides at right angle to each other. Hence (r) is correct.

3. Parallelogram is a quadrilateral which has equal opposite sides and both pair of opposite sides are parallel to each other. Hence (p) is correct.

4. Rhombus has all sides equal to each other but angle between sides isn't $$90^{\circ}$$ and opposite angles are equal. Hence (t) is correct.

5. Trapezium is a quadrilateral with only one pair of opposite sides parallel to each other. Hence (s) is correct.

Question 5
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If the diagonals of a quadrilateral bisect each other at right angle, then it is a __________.

A
Kite

B
Parallelogram

C
Rhombus

D
Rectangle

Solution

The diagonals of a Rhombus bisect each other at an angle of $$90^0$$ i.e. right angle.
Question 6
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Choose the correct statement.

A
The diagonals of a parallelogram are equal

B
The diagonals of a rectangle are perpendicular to each other

C
If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus

D
Every quadrilateral is either a trapezium or a parallelogram or a kite

Solution

$$\textbf{Step-1: Analyze the options}$$

$$\text{Option A: The diagonals of a parallelogram are not equal.}$$

$$\text{Option B: The diagonals of a rectangle are not perpendicular to each other.}$$

$$\text{Option C: The diagonals of a square, rhombus, kite bisect each other at right angles,}$$

$$\text{not strictly for rhombus only.}$$

$$\text{Option D : There exist many quadrilaterals- square, rectangle, rhombus}$$

$$\textbf{Step-2: Conclusion}$$

$$\text{So, we can say that only one of the given options, (C) is correct.}$$

$$\text{We can say that if diagonals of a rhombus bisect each other, it is not necessarily a rhombus.}$$

$$\textbf{Thus, the correct option is C.}$$
Question 7
1 / -0

If each pair of opposite sides of a quadrilateral are equal and parallel, then it is a ____________.

A
Kite

B
Trapezium

C
Parallelogram

D
None of these

Solution

if each pair of opposite sides of a quadrilateral is equal and parallel then it is a parallelogram (property of parallelogram)
Question 8
1 / -0

Choose the correct alternative :
For every quadrilateral there are............element

A
$$4$$

B
$$6$$

C
$$10$$

D
$$8$$

Solution

A Quadrilateral has 8 elements - 4 Sides and 4 Angles.
Question 9
1 / -0

The angle of a quadrilateral are in the ratio $$3 : 4 : 5 : 6$$. The largest of them is:

A
$${ 90 }^{ \circ }$$

B
$${ 120 }^{ \circ }$$

C
$${ 150 }^{ \circ }$$

D
$${ 102 }^{ \circ }$$

Solution

Given the ratio of angles of quadrilateral, $$ABCD$$ is $$3:4:5:6$$.
Let the angles of quadrilateral $$ABCD$$ be $$3x,4x,5x,6x$$, respectively.
We know, by angle sum property, the sum of angles of a quadrilateral is $$360^\circ$$.
$$\Rightarrow 3x+4x+5x+6x=360^\circ$$
$$\Rightarrow 18x=360^\circ$$
$$\therefore x=20^\circ$$.

$$\angle A =3x$$
$$=3 \times 20^\circ$$
$$ =60^\circ$$

$$ \angle B =4x$$
$$=4\times 20^\circ$$
$$ =80^\circ$$

$$ \angle C =5x$$
$$=5 \times 20^\circ $$
$$=100^\circ$$

$$ \angle D =6x$$
$$=6 \times 20^\circ$$
$$ =120^\circ$$

The largest angle is equal to $$120^\circ.$$ Hence, option $$B$$ is correct.
Question 10
1 / -0

If bisectors of $$\angle A$$ and $$\angle B$$ of a quadrilateral ABCD intersect each other at $$P$$, bisectors of $$\angle B$$ and $$\angle C$$ at $$Q$$, bisectors of $$\angle C$$ and $$\angle D$$ at $$R$$ and bisectors of $$\angle D$$ and $$\angle A$$ at $$S$$, then PQRS is a

A
rectangle

B
rhombus

C
parallelogram

D
quadrilateral whose opposite angles are supplementary

Solution

From question the diagram we get is above.
From figure,
$$\angle QPS = \angle APB$$ (Vertically opposite angles) ---- (1)
Consider, $$\triangle APB$$

$$\angle APB + \dfrac{1}{2}\angle A + \dfrac{1}{2}\angle B = 180^\circ$$

$$\angle APB = 180^\circ - \dfrac{1}{2} (\angle A + \angle B)$$ ----- (2)

From equation (1) & (2),
$$\angle QPS = 180^\circ - \dfrac{1}{2} (\angle A + \angle B)$$ ----- (3)
Similarly, $$\angle QRS = 180^\circ$$ - $$\dfrac{1}{2} (\angle C + \angle D)$$ ---- (4)
From (3) &(4),
$$\angle QPS + \angle QRS = 360^\circ$$ - $$\dfrac{1}{2} (\angle A + \angle B + \angle C + \angle D)$$
$$= 360^\circ - \dfrac{1}{2}(360^\circ)$$
$$= 360^\circ - 180^\circ$$
$$\therefore$$ $$\angle$$QPS + $$\angle$$QRS = $$180^\circ$$

Hence, PQRS is a quadrilateral whose opposite angles are supplementary.

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Quadrilaterals Test - 20

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Quadrilaterals Test - 20

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SHARING IS CARING

Question 1

adjacent

congruent

opposite

linear

Solution

Question 2

Rectangle

Rhombus

Triangle

Trapezium

Solution

Question 3

rectangle

rhombus

kite

square

Solution

Question 4

$$1\rightarrow (t), 2\rightarrow (s), 3\rightarrow (r), 4\rightarrow (p), 5\rightarrow (q)$$

$$1\rightarrow (p), 2\rightarrow (q), 3\rightarrow (r), 4\rightarrow (s), 5\rightarrow (t)$$

$$1\rightarrow (r), 2\rightarrow (q), 3\rightarrow (t), 4\rightarrow (p), 5\rightarrow (s)$$

$$1\rightarrow (q), 2\rightarrow (r), 3\rightarrow (p), 4\rightarrow (t), 5\rightarrow (s)$$

Solution

Question 5

Kite

Parallelogram

Rhombus

Rectangle

Solution

Question 6

The diagonals of a parallelogram are equal

The diagonals of a rectangle are perpendicular to each other

If the diagonals of a quadrilateral intersect at right angles, it is not necessarily a rhombus

Every quadrilateral is either a trapezium or a parallelogram or a kite

Solution

Question 7

Kite

Trapezium

Parallelogram

None of these

Solution

Question 8

$$4$$

$$6$$

$$10$$

$$8$$

Solution

Question 9

$${ 90 }^{ \circ }$$

$${ 120 }^{ \circ }$$

$${ 150 }^{ \circ }$$

$${ 102 }^{ \circ }$$

Solution

Question 10

rectangle

rhombus

parallelogram

quadrilateral whose opposite angles are supplementary

Solution

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