Free Quadrilaterals 03 Practice Test - 9th Grade
Question 1
In which of the following ways can four people hold each other's hands to form a quadrilateral?
All four stand in one line
Three stand in one line and one of them out of the line
Two pairs of people stand facing each other
Two pairs of people stand with their back facing and hold hands from behind and side.
SOLUTION
Solution : C and D
A figure formed by joining four points in an order is called a quadrilateral.
Consider the analogy of four people as four points.
In the first case, there are four collinear points which cannot form a quadrilateral.
In the second case, there are three collinear points which can form a triangle, but not a quadrilateral.
In the third case, the two pair of people face each other and thus form a quadrilateral.
In the fourth case, the two pair of people face exactly opposite but hold each others hands from behind and side and thus can for a quadrilateral.
Question 2
A parallelogram whose all sides are equal is called a _____.
trapezium
rhombus
rectangle
kite
SOLUTION
Solution : B
- Trapezium cannot be a parallelogram.
- Rhombus is a parallelogram, whose sides are always equal.
- Rectangle is a parallelogram whose opposite sides are equal.
- Kite is not a parallelogram.
A parallelogram whose all sides are equal is called a rhombus.
Question 3
The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.
40∘, 100∘, 80∘, 140∘
60∘, 80∘, 100∘, 120∘
30∘, 40∘, 50∘, 60∘
10∘, 20∘, 30∘, 40∘
SOLUTION
Solution : B
The angles of a quadrilateral are in the ratio 3:4:5:6.
Let the angles of the quadrilateral be 3x,4x,5x,6x.
The sum of the angles of a quadrilateral is 360∘.
⇒3x+4x+5x+6x=360∘
⇒18x=360∘
⇒x=20∘∴3x=60∘,4x=80∘,5x=100∘,6x=120∘
Question 4
The three angles of a quadrilateral are 40∘,80∘,90∘. The fourth angle is:
150∘
140∘
180∘
90∘
SOLUTION
Solution : A
According to the angle sum property of a quadrilateral, the sum of all the angles of a quadrilateral is =360∘
∴The fourth angle
=360∘-(40∘+80∘+90∘)
=360∘−210∘
=150∘
Question 5
Which of the following is a regular quadrilateral?
Parallelogram
Square
Trapezium
Kite
SOLUTION
Solution : B
A regular quadrilateral is a shape that has four equal sides with all the interior angles equal.
Among the given options, only square has all its four sides equal with each angle being 90∘.
Question 6
To determine all angles of a parallelogram, which of the following is the minimum necessary condition?
Only one angle is known.
Two angles are known.
Three angles are known.
Length of sides should be known
SOLUTION
Solution : A
If one angle of a parallelogram is known, the other angles can be found out by applying the following two properties:
1. The adjacent angles are supplementary.
2. The opposite angles are equal.
Question 7
Area of parallelogram is the product of base and corresponding height.
True
SOLUTION
Solution : A
A parallelogram is made up of two triangles, each having an area equal to the half of the product of base and corresponding height. Adding these two, we find the given statement to be true.
Question 8
If one of the angles of a parallelogram is 80°, the other non-adjacent angle is
SOLUTION
Solution :In a parallelogram, the opposite angles are equal. Hence, the non-adjacent angle is 80∘.
Question 9
Quadrilateral in which only one pair of opposite sides is parallel is known as
SOLUTION
Solution :Trapezium is a quadrilateral in which only one pair of opposite sides is parallel.
Question 10
A diagonal of a parallelogram divides it into two congruent triangles.
True
False
SOLUTION
Solution : A
Suppose ABCD is a parallelogram and BD is the diagonal.
There are two triangles - Δ ABD and Δ CDB
In Δ ABD and Δ CDB,
AD = BC (opposite sides of a parallelogram are equal)
AB = CD (opposite sides of a parallelogram are equal)
BD is common
∴ By SSS criterion of congruency,
Δ ABD ≅ Δ CDB
Hence, the given statement is true.
