Quadrilaterals Test

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Quadrilaterals Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements holds always?

A
Every rectangle is a square.

B
Every parallelogram is a trapezium.

C
Every rhombus is a square.

D
Every parallelogram is a rectangle.

Solution

option $$A$$
A square have all sides equal. A rectangle may have different adjacent but equal parallel sides.
So, rectangle can't be a square always.

option $$B$$
A parallelogram is always a trapezium.

option $$C$$
A rhombus does not always have angle of $$90^{o}$$ always.

option $$D$$
Parallelogram does not have all angles of $$90^{o}$$ always.

Hence, option B is correct.
Question 2
1 / -0

State true or false:
All squares are not parallelograms.

A
True

B
False

C
Ambiguous

D
Data Insufficient

Solution

Opposite sides of parallelogram are equal and parallel but all angles are not equal only opposite angles are equal. All sides and angles of a square are equal.
So, All squares are parallelograms.
Question 3
1 / -0

Can all the four angles of a quadrilateral be obtuse angle?

A
Yes

B
No

C
May be

D
Cannot be determined

Solution

$$\Rightarrow$$ An obtuse angle is greater than $$90^o$$ and by angle sum property, the sum of all four angles of a quadrilateral is $$360^o$$ .
$$\Rightarrow$$ If we take all four angles greater than $$90^o$$ then, there sum will be obviously greater than $$360^o$$.
Hence, all the four angles of a quadrilateral cannot be obtuse.
Therefore, option $$B$$ is correct.
Question 4
1 / -0

Find the unknown angle in the figure.

A
$$40^{0}$$

B
$$50^{0}$$

C
$$60^{0}$$

D
$$70^{0}$$

Solution

We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$.

The given angles are $$50^o,130^o,120^o,x$$.
Then, $$50^o+130^o+120^o+x=360^o$$.
Therefore, the unknown angle is:

$$\Rightarrow$$ $$360^o - (50^o + 130^o + 120^o ) =x^{\circ}$$

$$\Rightarrow$$ $$x^o=360^o - 300^o =60^{\circ}$$.

Therefore, the unknown angle is $$x^o=60^o$$.

Hence, option $$C$$ is correct.
Question 5
1 / -0

Can all the angles of a quadrilateral be right angles?

A
Yes

B
No

C
Maybe

D
Cannot be determined

Solution

Let us take a quadrilateral $$ABCD$$ with $$AC$$ as its diagonal.
In $$\Delta ADC$$ we have,
$$ \angle ACD+\angle CDA+\angle DAC={ 180 }^{ O }$$ ........$$(i) $$ [sum of the angles of a $$\Delta ={ 180 }^{ O }]$$
Also, in $$\Delta ABC$$ we have
$$ \angle ACB+\angle CBA+\angle BAC={ 180 }^{ O }$$ ........$$(ii) $$ [sum of the angles of a \Delta ={ 180 }^{ O }]$$ .

Adding $$(i)$$ & $$(ii)$$, we have,
$$ \angle ACD+\angle CDA+\angle DAC+\angle ACB+\angle CBA+\angle BAC={ 360 }^{ O }$$
$$\Longrightarrow \angle A+\angle B+\angle C+\angle D={ 360 }^{ O }$$
So, the sum of the angles of a quadrilateral is $${ 360 }^{ O }$$ .......$$(iii)$$.

Now, if each angle is $${ 90 }^{ o }$$, then $$\angle A+\angle B+\angle C+\angle D={ 90 }^{ O }\times 4={ 360 }^{ O }$$ .
It complies with $$(iii)$$.

Hence, all the angles of a quadrilateral can be right angles.
That is, the statement is true.
Therefore, option $$A$$ is correct.
Question 6
1 / -0

State true or false:
All kites are rhombuses.

A
True

B
False

C
Ambiguous

D
Data Insufficient

Solution

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other and only one pair of opposite angles are equal.
All sides of a rhombus are equal and opposite angles are equal.
So, all kites are not rhombuses.
Question 7
1 / -0

The value of $$x$$ in the given diagram is ?

A
$$130^{o}$$

B
$$140^{o}$$

C
$$150^{o}$$

D
$$160^{o}$$

Solution

We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$.

The given angles are $$70^o,60^o,90^o,x$$. ......[Linear pairs are supplementary]
Then, $$70^o+60^o+90^o+x=360^o$$.
Therefore, the unknown angle is:
$$\Rightarrow$$ $$360^o - (70^o + 60^o + 90^o ) =x^{\circ}$$
$$\Rightarrow$$ $$x^o=360^o - 220^o =140^{\circ}$$.

Therefore, the unknown angle is $$x^o=140^o$$.
Hence, option $$B$$ is correct.
Question 8
1 / -0

All squares are rhombuses and also rectangles.

A
True

B
False

C
Ambiguous

D
Data Insufficient

Solution

The diagonals of square bisect each other at $$90^{\circ}$$, same as rhombus. Hence, all squares are rhombuses.
The adjacent sides of square are perpendicular to each and the opposite sides are equal and parallel to each other, same as rectangles. Hence, all squares are rectangles too.

Hence, the given statement is $$True$$.
Question 9
1 / -0

All rhombuses are parallelograms?

A
True

B
False

C
Ambiguous

D
Data Insufficient

Solution

Opposite sides of a parallelogram are equal but all sides of a rhombus are equal. So, rhombus is a parallelogram but parallelogram is not a rhombus.
Question 10
1 / -0

State true or false:
All squares are trapeziums.

A
True

B
False

C
Ambiguous

D
Data Insufficient

Solution

Since, one of the opposite pairs of lines of a squares is parallel. Hence, all squares are trapeziums.

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Quadrilaterals Test - 16

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Quadrilaterals Test - 16

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Question 1

Every rectangle is a square.

Every parallelogram is a trapezium.

Every rhombus is a square.

Every parallelogram is a rectangle.

Solution

Question 2

True

False

Ambiguous

Data Insufficient

Solution

Question 3

Yes

No

May be

Cannot be determined

Solution

Question 4

$$40^{0}$$

$$50^{0}$$

$$60^{0}$$

$$70^{0}$$

Solution

Question 5

Yes

No

Maybe

Cannot be determined

Solution

Question 6

True

False

Ambiguous

Data Insufficient

Solution

Question 7

$$130^{o}$$

$$140^{o}$$

$$150^{o}$$

$$160^{o}$$

Solution

Question 8

True

False

Ambiguous

Data Insufficient

Solution

Question 9

True

False

Ambiguous

Data Insufficient

Solution

Question 10

True

False

Ambiguous

Data Insufficient

Solution

User

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