Free Understanding Quadrilaterals 03 Practice Test - 8th Grade
Question 1
Which among the following has the most number of diagonals?
Triangle
Quadrilateral
Pentagon
Can't be determined
SOLUTION
Solution : C
The pentagon has the most number of vertices among the options. Hence, it has the most number of diagonals.
Question 2
In the given diagram, the value of x is
SOLUTION
Solution : In quadrilateral ABCD,
∴∠ABC+∠BCD+∠CDA+∠DAB=360∘40∘+50∘+∠CDA+70∘=360∘⇒∠CDA+160∘=360∘⇒∠CDA=360∘−160∘=200∘
Now, ∠CDA+∠ADC=360∘ (∵ Angle at a point)
200∘+x=360∘⇒x=360∘−200∘⇒x=160∘
Question 3
In a concave polygon, no part of any of their diagonals is external.
True
False
SOLUTION
Solution : B
A concave polygon will have some part of at least one diagonal external.
Question 4
Which of the following are definitely regular polygons?
Triangle
Square
Rhombus
Rectangle
SOLUTION
Solution : B
A regular polygon is a polygon which is equiangular i.e. all the angles are equal and equilateral i.e. all the sides are equal.
The triangle if equilateral is a regular polygon. If not, it is not a regular polygon.
A rhombus has equal sides but not equal angles.
A Rectangle has equal angles but not equal sides. Hence, they are not regular polygons.
A square has equal sides and equal angles. Hence, it is a regular polygon.
Question 5
Which of the following is true?
All squares are rectangles
All rectangles are squares
All rectangles are rhombuses
SOLUTION
Solution : A
The statement that all squares are rectangles is true because a square is a special type of rectangle where, the adjacent sides are equal.
Question 6
If ABCD is a parallelogram, then the angle bisectors of ∠A and ∠D meet at ‘O’. The measure of ∠AOD is 45∘
True
False
SOLUTION
Solution : B
Let∠A=x∘
then ∠D=(180−x)∘
(Since the adjacent angles of a parallelogram sum up to 180∘)
∴∠A2=x2=∠DAO
and∠D2=(180−x)2=90−x2=∠ADO
In ΔAOD,
∠AOD+∠ADO+∠DAO=180∘ [Angle sum property of a triangle]
∠AOD=180∘−[∠ADO+∠DAO]
∠AOD=180∘−[x2+90−x2]
or ∠AOD=180−90=90∘
∴ The measure of ∠AOD is 90∘
Question 7
Which of the following is not a model for a plane surface?
Top surface of table
Surface of paper
Body of car
None of these
SOLUTION
Solution : C
The body of a car is a 3 dimensional surface. It is not a plane 2 dimensional surface
Question 8
A quadrilateral with two distinct pairs of equal-length adjacent sides is known as
SOLUTION
Solution : D
A quadrilateral with two distinct pairs of equal-length adjacent sides is known as a kite.
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Question 9
Two sides of a kite have lengths 7.8 cm and 11 cm. Then the perimeter of the kite is
SOLUTION
Solution : C
Let ‘a’ be one side of the kite = 7.8 cm
and‘b’ be the other side of the kite = 11 cm
Perimeter of the kite = 2a + 2b units
=2×7.8+2×11=15.6+22=37.6 cm
Question 10
Which of the following is true?
All parallelograms are kites
All kites are parallelograms
Some kites are parallelograms
SOLUTION
Solution : C
The kites that have all the sides equal and two pairs of sides parallel are parallelograms. These kites are rhombuses.
Hence, some kites are parallelograms.