MCQ(1M)

MCQ 511 Mark

If $\text{ABCD}$ is a parallelogram with two adjacent angles $\angle\text{A}=\angle\text{B}$ then the parallelogram is a:

A
Rhombus.
B
Trapezium.
✓
Rectangle.
D
None of these.

Answer

Correct option: C.

Rectangle.

Given that $\text{ABCD}$ is a parallelogram.
We konw that, opposite sides of a parallelogram are parallel.
$\Rightarrow\angle\text{A}+\angle\text{B}=180^{\circ} ...($interior angles$)$
Also, $\angle\text{A}=\angle\text{B}=90^{\circ} ...($Given$)$
Since opposite angles of a parallelogram are equal,
$\angle\text{A}=\angle\text{C}$ and $\angle\text{B}=\angle\text{D}$
So, $\angle\text{A}=\angle\text{C}=\angle\text{B}=\angle\text{D}=90^{\circ}$
$\therefore \text{ABCD}$ is a rectangle.

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MCQ 521 Mark

The figure formed by joining the mid $-$ points of the adjacent sides of a rectangle is a:

✓
Rhombus.
B
Square.
C
Rectangle.
D
Parallelogram.

Answer

Correct option: A.

Rhombus.

The figure formed by joining the mid points of the adjacent sides of a rectangle is a rhombus.

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Question 531 Mark

Short Answer Questions.
Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reasons for your answer.

Answer

The given statement is false.
Diagonals of a parallelogram bisect each other.

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MCQ 541 Mark

$\text{ABCD}$ is a rhombus such that $\angle\text{ACB}=50^{\circ}.$ Then, $\angle\text{ADB}=?$

✓
$40^\circ$
B
$25^\circ$
C
$65^\circ$
D
$130^\circ$

Answer

Correct option: A.

$40^\circ$

$\text{ABCD}$ is a rhombus.
$\Rightarrow AD \| BC$ and $\text{AC}$ is the transversal.
$\Rightarrow\angle\text{DAC}=\angle\text{ACB} \ ($alternate angles$)$
$\Rightarrow\angle\text{DAC}=50^{\circ}$
In $\triangle\text{AOD},$ by angle sum property,
$\angle\text{AOD}+\angle\text{DAO}+\angle\text{ADO}=180^{\circ}$
$\Rightarrow90^{\circ}+\angle\text{50}^{\circ}+\angle\text{ADO}=180^{\circ}$
$\Rightarrow\angle\text{ADO}=40^{\circ}$
$\Rightarrow\angle\text{ADB}=40^{\circ}$

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MCQ 551 Mark

In a quadrilateral $\text{ABCD}$, if $AO$ and $BO$ are the bisectors of $\angle\text{A}$ and $\angle\text{B}$ respectively, $\angle\text{C}=70^{\circ}$ and $\angle\text{D}=30^{\circ}.$ Then, $\angle\text{AOB}=?$

A
$40^\circ$
✓
$50^\circ$
C
$80^\circ$
D
$100^\circ$

Answer

Correct option: B.

$50^\circ$

We know that, sum of the angles of a quadrilateral is $360^\circ .$
$\Rightarrow\angle\text{A}+\angle\text{B}+\angle\text{C}+\angle\text{D}=360^{\circ}$
$\Rightarrow\angle\text{A}+\angle\text{B}+70^{\circ}+30^{\circ}=360^{\circ}$
$\Rightarrow\angle\text{A}+\angle\text{B}=260^{\circ}$
$\Rightarrow\frac{1}{2}\angle\text{A}+\frac{1}{2}\angle\text{B}=\frac{1}{2}(260)^{\circ}$
$\Rightarrow\angle\text{BAO}+\angle\text{ABO}=130^{\circ}...(\text{i})$
In $\triangle\text{AOB},$
$\angle\text{BAO}+\angle\text{ABO}+\angle\text{AOB}=180^{\circ} ... ($Angle sum Property)
$\Rightarrow130^{\circ}+\angle\text{AOB}=180^{\circ} ... ($from $(i))$
$\Rightarrow\angle\text{AOB}=50^{\circ}$

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MCQ 561 Mark

Is quadrilateral $\text{ABCD} \ a \| gm$?
$(i) $Diagonals $AC$ and $BD$ bisect each other.
$(ii)$ Diagonals $AC$ and $BD$ are equal.

✓
If the question can be answered by one of the given statements alone and not by the other;
B
If the question can be answered by either statement alone;
C
If the question can be answered by both the statements together but not by any one of the two;
D
If the question cannot be answered by using both the statements together.

Answer

Correct option: A.

If the question can be answered by one of the given statements alone and not by the other;

If the diagonals of a quad. $\text{ABCD}$ bisect each other, then the quad. $\text{ABCD}$ is a parallelogram.
So, $I$ gives the answer.
If the diagonals are equal, then the quad. $\text{ABCD}$ is a parallelogram.
So, $II$ gives the answer.

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Maths MCQ(1M)