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CBSE Questions for Class 8 Maths Understanding Quadrilaterals Quiz 2 - MCQExams.com
CBSE
Class 8 Maths
Understanding Quadrilaterals
Quiz 2
Two adjacent sides of a parallelogram are $$6$$ cm and $$8$$ cm. Its perimeter is
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$$28$$ cm
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$$26$$ cm
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$$14$$ cm
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None of these
Explanation
perimeter of ll gm $$=$$ sum of all sides
$$=8 + 8 + 6 + 6$$
$$=28$$ cm.
Number of pairs of parallel lines in a trapezium is:
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$$1$$
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$$2$$
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$$3$$
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$$4$$
Explanation
A trapezium has one pair of parallel lines as shown in the figure.
So option $$A$$ is correct.
Explain how square is a
parallelogram.
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sum of all angles is $$90^o$$
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All angles are equal
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Opposites sides are parallel
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None of these
Explanation
$$\Rightarrow$$ A parallelogram is a quadrilateral with two pairs of opposite sides.
$$\Rightarrow$$ In square we know that, all sides are equal which means opposite sides are equal.
$$\Rightarrow$$ And in square opposite sides are parallel.
$$AB=DC=8 cm, AD=4 cm$$ what should be the length of side $$BC$$, if $$ABCD$$ is parallelogram
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$$4cm$$
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$$8cm$$
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$$16cm$$
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None of the above
Explanation
As $$ABCD$$ is parallelogram so opposite sides should be equal
$$\Rightarrow AD=BC$$
$$\therefore BC=4cm$$
The ratio of measures of opposite angles of any parallelogram is
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$$1 : 2$$
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$$1 : 1$$
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$$2 : 3$$
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$$1 : 3$$
Explanation
According to the definition of a parallelogram, opposite angles of any parallelogram are congruent.
In any parallelogram $$ABCD,\ \ \angle A=\angle C$$ , and $$\angle B=\angle D.$$
Hence, the ratio of opposite angles of any parallelogram is $$1:1.$$
Can a quadrilateral ABCD be a parallelogram if
$$\angle A=70^o$$ and $$\angle C=65^o$$
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True
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False
Explanation
Since $$ \angle A \not= \angle C $$, i.e., the opposite angles are unequal, so ABCD is not a parallelogram.
State true or false:
PQRS is a parallelogram and $$\angle 1$$ and $$\angle 2$$ are two exterior,angles, then $$\angle 1=\angle 2$$
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True
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False
Explanation
$$\quad PQRS\quad is\quad given\quad parallelogram\quad \\ \angle 1+\angle QRS\quad =\quad 180(Linear\quad pair\quad of\quad angles)......(1)\\ \quad \angle 2\quad +\quad \angle SPQ\quad =\quad 180(Linear\quad pair\quad of\quad angles).......(2)\\ also,\quad \angle QRS\quad =\quad \angle SPQ\quad (opposite\quad angles\quad of\quad \parallel gram\quad are\quad equal).......(3)\\ \Longrightarrow \angle 1\quad +\quad \angle SPQ\quad =\quad 180(From\quad (3)\quad ..........(4)\quad \quad \\ Subtracting\quad eq(2)\quad and\quad eq(4)\quad we\quad get\\ \Longrightarrow \angle 1\quad -\angle 2\quad =\quad 0\\ \Longrightarrow \angle 1\quad =\quad \angle 2\\ Hence\quad proved$$\\
The diagonals of a parallelogram ABCD intersect at O. If $$\angle BOC =90^o$$ and $$\angle BDC = 50^o$$, then $$\angle AOB$$ is
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$$10^o$$
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$$40^o$$
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$$50^o$$
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$$90^o$$
Explanation
It is given that angle BOC = 90.
It means the diagonals cut each other at a right angle.
Angle AOB= 180- Angle BOC =90
So, angle AOB = angle BOC
= 90.
So the correct answer is option D.
The data that $$\angle BDC = 50^{\circ}$$ is not required.
In a parallelogram ABCD, AB > AD. Then
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$$\displaystyle \angle ADB=\angle DBC$$
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$$\displaystyle \angle CBD=\angle DAB$$
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$$\displaystyle \angle ADB<\angle BDC$$
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$$\displaystyle \angle ADB>\angle BDC$$
Explanation
$$\displaystyle AB>AD$$
$$\displaystyle \therefore \quad \angle ADB>\angle ABD$$ (angle opposite to longer side is greater)
$$\displaystyle \therefore \quad \angle ADB>\angle BDC$$ ($$\displaystyle \because \quad \angle ABD=\angle BDC$$ as ABCD is a parallelogram)
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram
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$$90^o$$
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$$120^o$$
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$$70^o$$
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$$80^o$$
Explanation
Let $$ABCD$$ be the parallelogram with $$\angle A=\angle B.$$
We know, sum of adjacent angles of parallelogram is $$180^o.$$
$$\Rightarrow$$ $$\angle A+\angle B=180^o$$
$$\Rightarrow$$ $$2\angle A=180^o$$ [ Since, $$\angle A=\angle B$$ ]
$$\Rightarrow$$ $$\angle A=90^o$$
$$\Rightarrow$$ $$\angle B=\angle A=90^o$$
$$\Rightarrow$$ $$\angle A=\angle C=90^o$$ [ Opposite angles of parallelogram ]
$$\Rightarrow$$ $$\angle B=\angle D=90^o$$ [ Opposite angles of parallelogram ]
$$\therefore$$ Each angle of the parallelogram measures is $$90^o.$$
What is a curve?
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It is an angle
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It is a polygon
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It is a quadrilateral
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It is a shape or a line which is smoothly drawn in a plane having a bent or turns in it.
Explanation
A curve is a shape or a line which is smoothly drawn in a plane having a bent or turns in it.
Hence, D will be correct answer.
Which of the following is an example of an open curve?
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Circle
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Triangle
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A line segment
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Pentagon
Explanation
As the line segment has two end points, so it is an open curve.
Therefore, C is the correct answer.
The diagonals of a convex polygon are always in the ______ of the polygon.
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interior
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exterior
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Either
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None of these
Explanation
The angles are less than $$180^o$$ and the vertices of a polygon with points outward. While joining two vertices they will move inwards i.e the diagonal.
Therefore, A is the correct answer.
The vertices of a convex polygon point are .....................
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outwards
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inwards
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middle
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extreme corner
Explanation
As the angles of a convex polygon are less than $$180^o$$, the vertices points outwards.
Therefore, A is the correct answer.
A closed curve has no _____.
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joints
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starting point
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end point
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All of the above
Explanation
The beginning point and the ending point in a closed curve is the same. There are no end point and starting point. For example: Circle, square.
Therefore, B and C is the correct answer.
When you draw without lifting your pencil or pen on a paper you get?
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Plane curve
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Plane shadow
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3-dimension
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Line
Explanation
When we join number of points without lifting our pen we make a shape which not necessarily should be straight or curve. We get a plane curve.
Therefore, A is the correct answer.
A curve which has 2 end points is called an .....................
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closed curve
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simple curve
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open curve
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None of the above
Explanation
An open curve is a curve whose end points do not join. In other words it has 2 end points.
Therefore, C is the correct answer.
The closed curve that crosses _____ is not a simple closed curve.
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twice
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itself
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multiple points
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All of the above
Explanation
The closed curve that doesn't crosses itself is a simple closed curve.
So, t
he closed curve that crosses itself is not a simple closed curve.
Therefore, $$Op-B$$ is the correct answer.
Convex polygon does not have portions of their diagonals in their ................. .
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exterior
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interior
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edges
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boundary
Explanation
Diagonals are which join two opposite vertices. A polygon is a closed figure, so their diagonals do not extend in their exterior. Such figures are convex polygon.
Therefore, A is the correct answer.
A parallelogram is a quadrilateral whose ...................... sides are parallel.
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adjacent
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congruent
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opposite
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linear
Explanation
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.
A polygon with at least one .................. angle is called concave polygon.
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obtuse angle
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acute
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reflex
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straight
Explanation
A polygon having at least 1 angle more than $$180^o$$ and vertices pointing inwards is called a concave polygon.
Therefore, C is the correct answer.
A concave polygon has .................... interior angles more than $$180^o$$.
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no
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3 angles
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one or more
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less than 5
Explanation
All angles less than $$180^o$$ is a convex polygon. Convex is opposite of concave, so at least one angle has to be more than $$180^o$$ to be a concave polygon.
Therefore, C is the correct answer.
A parallelogram each of whose angle measures $$90^\circ$$ is
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Rectangle
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Rhombus
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Triangle
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Trapezium
Explanation
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.
Name the parallel sides in the given parallelogram.
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$$EF \parallel HG$$
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$$EH \parallel FG$$
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$$EF \parallel SG$$
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Both A & B
Explanation
The opposite sides of a parallelogram are EF II HG and EH II FG.
Therefore, D is the correct answer.
In the given figure, identify the adjacent sides of a parallelogram.
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$$\overleftrightarrow{AD}$$ is adjacent to $$\overleftrightarrow{AB}$$ & $$\overleftrightarrow{DC}$$
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$$\overleftrightarrow{DC}$$ is adjacent to $$\overleftrightarrow{AD}$$ & $$\overleftrightarrow{BC}$$
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$$\overleftrightarrow{AB}$$ is adjacent to $$\overleftrightarrow{AD}$$ & $$\overleftrightarrow{BC}$$
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All of the above
Explanation
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.
All parallelograms are quadrilaterals.
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True
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False
Explanation
Yes it is true because the definition of quadrilaterals says that
In Euclidean plane geometry, a
quadrilateral
is a polygon with four edges (or sides) and four vertices or corners.
Students in a class were having arguments regarding the properties of the quadrilaterals. Choose the right argument.
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Student A - Rectangle is a Kite
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Student B - Rectangle is parallelogram
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Student C - Rectangle is a square
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Student D - Rectangle is a rhombus
Explanation
As the parallelogram, rectangle has opposite equal sides and opposite equal angles.
Therefore, B is the correct answer.
Polygons that have no portions of their diagonals in the exterior are called ____
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squares.
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regular pentagons.
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convex polygons.
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concave polygons.
Explanation
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
If $$\overline {AC}$$ and $$\overline {BD}$$ intersect at O such that $$AO = CO$$ and $$BO = DO$$, identify the correct option
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$$BC = AD$$
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$$BC \parallel AD$$ and $$BC = AD$$
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$$BC \parallel AD$$
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None of these
Explanation
By using properties of parallelogram i.e. - diagonals of parallelogram bisects each other . Hence $$ABCD$$ is a parallelogram.
$$\Rightarrow \boxed{BC||AD}$$
A rectangle is a .................. quadrilateral.
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concave
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irregular
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convex
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none of the above
Explanation
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.
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