Understanding Quadrilaterals Test

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Understanding Quadrilaterals Test - 10

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Question 1
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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 2
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In the given figure, identify the adjacent sides of a parallelogram.

A
$$\overleftrightarrow{AD}$$ is adjacent to $$\overleftrightarrow{AB}$$ & $$\overleftrightarrow{DC}$$

B
$$\overleftrightarrow{DC}$$ is adjacent to $$\overleftrightarrow{AD}$$ & $$\overleftrightarrow{BC}$$

C
$$\overleftrightarrow{AB}$$ is adjacent to $$\overleftrightarrow{AD}$$ & $$\overleftrightarrow{BC}$$

D
All of the above

Solution

In a parallelogram, the sides which are parallel are called as pair of opposite sides and others are adjacent to the first side.
In parallelogram $$ABCD$$, the pair of opposite sides are $$AB, CD$$ and $$AD, BC$$.
$$\therefore$$ $$AD$$ is adjacent to $$AB$$ and $$DC$$
$$DC$$ is adjacent to $$AD$$ and $$BC$$
$$AB$$ is adjacent to $$AD$$ and $$BC$$.
Hence, all the above are adjacent sides of a parallelogram.
Question 3
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Polygons that have no portions of their diagonals in the exterior are called ____

A
squares.

B
regular pentagons.

C
convex polygons.

D
concave polygons.

Solution

A convex polygon is defined as a polygon with all its interior angles less than $$180^o$$. This means that all the vertices of the polygon will point outwards, away from the interior of the shape.
Hence all diagonals of $$convex \ polygons$$ are $$interior$$.

$$Squares$$ and $$regular\ pentagons$$ are special types of $$convex \ polygons$$.
So option $$C$$ is correct
Question 4
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Students in a class were having arguments regarding the properties of the quadrilaterals. Choose the right argument.

A
Student A - Rectangle is a Kite

B
Student B - Rectangle is parallelogram

C
Student C - Rectangle is a square

D
Student D - Rectangle is a rhombus

Solution

As the parallelogram, rectangle has opposite equal sides and opposite equal angles.
Therefore, B is the correct answer.
Question 5
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A parallelogram with equal angles is called a ..............................

A
triangle

B
kite

C
rectangle

D
rhombus

Solution

$$Rectangle$$ is the only parallelogram which like a parallelogram has opposite sides parallel and all angles $$equal$$.
Therefore, C is the correct answer.
Question 6
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If $$\overline {AC}$$ and $$\overline {BD}$$ intersect at O such that $$AO = CO$$ and $$BO = DO$$, identify the correct option

A
$$BC = AD$$

B
$$BC \parallel AD$$ and $$BC = AD$$

C
$$BC \parallel AD$$

D
None of these

Solution

By using properties of parallelogram i.e. - diagonals of parallelogram bisects each other . Hence $$ABCD$$ is a parallelogram.
$$\Rightarrow \boxed{BC||AD}$$
Question 7
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A rectangle is a .................. quadrilateral.

A
concave

B
irregular

C
convex

D
none of the above

Solution

Solution:- As the diagonals are in the interior of the figure and its vertex are raised it is a convex.
Therefore, C is the correct answer.
Question 8
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Name the parallel sides in the given parallelogram.

A
$$EF \parallel HG$$

B
$$EH \parallel FG$$

C
$$EF \parallel SG$$

D
Both A & B

Solution

The opposite sides of a parallelogram are EF II HG and EH II FG.
Therefore, D is the correct answer.
Question 9
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In the figure at right, $$ABCD$$ is a parallelogram $$\angle BAO = 30^{\circ},\ \angle DAO=\angle 45^{\circ}$$ and $$\angle COD = 105^{\circ}$$. Calculate
$$\angle ABO$$

A
$$45^{\circ}$$

B
$$55^{\circ}$$>

C
$$25^{\circ}$$

D
$$None\ of\ these$$

Solution

$$\angle AOB = \angle DOC = 105^{\circ}$$
In the triangle AOB
Sum of all angles of a triangle $$= 180^{\circ} $$
$$\therefore \angle AOB + \angle ABO + \angle BAO = 180^{\circ}$$
$$\therefore 105 + \angle ABO + 30 = 180 $$
$$\angle ABO = 180 - 30 -105$$
$$\therefore \angle ABO = 45^{\circ}$$
Question 10
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The given polygon EFGH is a _____________.

A
Parallelogram

B
Concave polygon

C
Convex polygon

D
Trapezium

Solution

A polygon having an angle that exceeds $$180^\circ$$ is known as a concave polygon.
Since, the given diagram has $$\angle GHE > 180^\circ$$
So, given polygon $$EFGH$$ is a concave polygon.

Hence, option B is correct.