Understanding Quadrilaterals Test

Result

Understanding Quadrilaterals Test - 20

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Square is not a

A
rhombus

B
rectangle

C
trapezium

D
parallelogram

Solution

$$\textbf{Step-1: Comparing with trapezium}$$
$$\text{The definition of a square does not comply with the}$$
$$\text{definition of a trapezoid. The definition of a trapezoid}$$
$$\text{is a quadrilateral (a closed plane figure with 4 sides) with exactly one pair of parallel sides.}$$
$$\textbf{Step-2: Comparing with other option}$$
$$\text{On the other hand, a square is a very special kind of}$$
$$\text{quadrilateral; A square is also a parallelogram because}$$
$$\text{it has two sets of parallel sides and four right angles. A}$$
$$\text{square is also a parallelogram because opposite sides}$$
$$\text{are parallel. A square is always a rhombus. A rhombus}$$
$$\text{is a quadrilateral with four congruent sides. If the rhombus has 4}$$
$$\text{right angles it may also be called a square. So every square is a rhombus.}$$
$$\textbf{Hence , Square is not a (C) trapezium}$$
Question 2
1 / -0

If $$ABCD$$ is a quadrilateral, $$E, F, G$$ snd $$ H$$ are the midpoints of $$AB, BC, CD$$ and $$DA$$ respectively, then $$EFGH$$ is a ____ .

A
rectangle

B
square

C
rhombus

D
parallelogram

Solution
Question 3
1 / -0

In the figure above ABCD is a parallelogram $$\displaystyle \overline{DE}, \overline{EF}$$ and $$\displaystyle \overline{BG}$$ are the bisectors of $$\displaystyle \angle ADC, \angle DEB$$ and $$\displaystyle \angle ABC$$ respectively. BG and EF intersect at H. If $$\displaystyle \angle DAB=70^{\circ}$$ then find $$\displaystyle \angle BHE$$

A
$$\displaystyle 50^{\circ}$$

B
$$\displaystyle \left ( 62\frac{1}{2} \right )^{\circ}$$

C
$$\displaystyle 75^{\circ}$$

D
$$\displaystyle \left ( 87\frac{1}{2} \right )^{\circ}$$

Solution

Given $$\angle BAD =70^{\circ}$$
So $$\angle ADC = \angle ABC =180-70 = 110^{\circ}$$ (Sum of angles formed at adjacent vertices of parallelogram)
$$\angle ADE = half of angle ADC =55 degree
For triangle ADE , exterior angle DEB = angle DAE + angle ADE
= 70 + 55 = $$125^{\circ}$$
Now angle HEB is half of angle DEB
Thus $$\angle HEB = \frac{125}{2} = 62.5^{\circ}$$
Angle HBC = half of angle ABC = $$55 ^{\circ}$$
In triangle HEB
$$\angle EHB = 180^{\circ}- \angle HEB - \angle HBE$$
=180 - 62.5- 55
= $$62.5^{\circ}$$
So the correct answer is option B
Question 4
1 / -0

If $$ABCD$$ is a parallelogram whose diagonals intersect at $$O$$ and $$\Delta$$BCD is an equilateral triangle having each side of length $$6$$ cm, then the length of diagonal $$AC$$ is ____ .

A
$$3 \sqrt 3\ cm$$

B
$$6 \sqrt 3\ cm$$

C
$$3 \sqrt 6\ cm$$

D
$$12\ cm$$

Solution

$$ABCD$$ is a parallelogram.
∴$$BC=AD=6\ cm $$
and $$AB=DC=6\ cm$$,
Triangle $$BCD$$ is equilateral triangle
then $$BD=6\ cm$$
Hence $$ABCD$$ becomes a rhombus.
∴ Diagonals $$AC$$ and $$BD$$ bisect each other at right angle.
$$\therefore OD=\dfrac{1}{2}BD=\dfrac{6}{2}=3\ cm$$
$$\Delta OCD$$
$$(OC)^{2}=CD^{2}-(OD)^{2}=(6)^{2}-(3)^{2}=36-9=27$$
$$\therefore OC=3\sqrt{3}$$
$$\therefore AC=2\times OC=2\times 3\sqrt{3}=6\sqrt{3}\ cm$$
Question 5
1 / -0

If the adjacent angles of the parallelogram are $$x +30^\circ$$ and $$2x- { 90 }^{ \circ}$$, then the smaller angle is

A
$${ 110 }^{\circ }$$

B
$${ 100 }^{\circ }$$

C
$${ 70 }^{\circ }$$

D
$${ 80 }^{\circ }$$

Solution

In a parallelogram the adjacent angles are supplementary:
$$x+30^\circ+2x-90^\circ=180^\circ$$
$$\Rightarrow 3x=240^\circ$$
$$\Rightarrow x=80^\circ$$
Therefore, angles are:
$$x+30^\circ= 80^\circ+30^\circ=110^\circ$$ and
$$2x-90^\circ=2\times80^\circ-90^\circ=70^\circ$$
Therefore, smaller angle is $$70^\circ$$.
Option C is correct.
Question 6
1 / -0

Two adjacent angles of a parallelogram are $$2x+ 30^o$$ and $$5x + 30^o$$. Then the value of $$x$$ is ___ .

A
$$\dfrac{180^o}{7}$$

B
$$\dfrac{120^o}{7}$$

C
$$\dfrac{60^o}{7}$$

D
None of these.

Solution

Sum of two adjacent angles in a parallelogram is $$180^o$$.
$$\therefore \ 2x + 30^o + 5x + 30^o = 180^o$$
$$\Rightarrow 7x+60^o=180^o$$
$$\Rightarrow 7x = 120^o$$
$$\Rightarrow x = \dfrac{120^o}{7}$$
Question 7
1 / -0

If $$x$$ & $$y$$ are opposite angles of a parallelogram. If the adjacent angle to these angles is $$75^o$$. What is the measure of these angles?

A
$$110^o$$

B
$$150^o$$

C
$$85^o$$

D
$$105^o$$

Solution

One opposite angle is adjacent to $$75^o$$ angle. So, $$180^o-75^o=105^o$$
This is the measure of opposite angle. So, opposite angles being equal have same measure $$105^o$$.
Therefore, D is the correct answer.
Question 8
1 / -0

If the perimeter of a parallelogram is $$50\ cm$$ and one side is $$12\ cm$$. what is the measure of the other side ?

A
$$15\ cm$$

B
$$10\ cm$$

C
$$13\ cm$$

D
$$18\ cm$$

Solution

Perimeter $$= S_1 + S_2 + S_3 + S_4$$

$$50 = 12 + S_2 + 12 + S_4$$

$$\Rightarrow 50 - 24 = 2S$$

$$\Rightarrow \dfrac{26}{2} = S$$

$$\therefore 13 = S$$ (other side of the parallelogram)
Therefore, $$C$$ is the correct answer.
Question 9
1 / -0

In the measure of an angle in a parallelogram is $$110^o$$, what will be the measure of its adjacent angle?

A
$$110^o$$

B
$$80^o$$

C
$$70^o$$

D
$$250^o$$

Solution

Sum of angles $$=360^o$$
$$\angle A + \angle B + \angle C + \angle D = 360^o$$
$$\Longrightarrow110^o+x+110^o+x= 360^o$$
$$\Longrightarrow2x = 360^o - 220^o$$
$$\Longrightarrow x = 70^o$$
Therefore, C is the correct answer.
Question 10
1 / -0

Identify the Quadrilateral.

A
parallelogram

B
rectangle

C
square

D
trapezium

Solution

It is a trapezium as it has no equal sides, no right angles, opposite angles are not equal. It cannot be a parallelogram, rectangle or square.
Therefore, D is the correct answer.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Understanding Quadrilaterals Test - 20

Result

Understanding Quadrilaterals Test - 20

Score

-

Rank

-

SHARING IS CARING

Question 1

rhombus

rectangle

trapezium

parallelogram

Solution

Question 2

rectangle

square

rhombus

parallelogram

Solution

Question 3

$$\displaystyle 50^{\circ}$$

$$\displaystyle \left ( 62\frac{1}{2} \right )^{\circ}$$

$$\displaystyle 75^{\circ}$$

$$\displaystyle \left ( 87\frac{1}{2} \right )^{\circ}$$

Solution

Question 4

$$3 \sqrt 3\ cm$$

$$6 \sqrt 3\ cm$$

$$3 \sqrt 6\ cm$$

$$12\ cm$$

Solution

Question 5

$${ 110 }^{\circ }$$

$${ 100 }^{\circ }$$

$${ 70 }^{\circ }$$

$${ 80 }^{\circ }$$

Solution

Question 6

$$\dfrac{180^o}{7}$$

$$\dfrac{120^o}{7}$$

$$\dfrac{60^o}{7}$$

None of these.

Solution

Question 7

$$110^o$$

$$150^o$$

$$85^o$$

$$105^o$$

Solution

Question 8

$$15\ cm$$

$$10\ cm$$

$$13\ cm$$

$$18\ cm$$

Solution

Question 9

$$110^o$$

$$80^o$$

$$70^o$$

$$250^o$$

Solution

Question 10

parallelogram

rectangle

square

trapezium

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.