Free Practical Geometry 01 Practice Test - 6th grade 

Question 1

Draw a circle with center O with radius 5 cm. Draw any one of the diameters. With same center A, draw another circle with radius 3 cm. Draw any one of the diameters for this circle too. If you join the ends of both the diameters, the figure you will get is:

A.

Parallelogram

B.

Rectangle

C.

Square

D.

Trapezium

SOLUTION

Solution : A

Draw the circles and the diameters. You will get:

 

If you mark the diameter of smaller circle as AB and larger circle as CD, after joining them you will get:

 

 

Fig. ABCD is a parallelogram. When AB is perpendicular to CD, ABCD becomes a rhombus.

Question 2

If AB is perpendicular to CD and PQ is perpendicular to AB, which of the following is/are true?

A.

CD is parallel to PQ

B.

CD is perpendicular to PQ

C.

Both A & B

D.

None of the above 

SOLUTION

Solution : A

If you draw everything according to the given question, you would get: 

 

We can see that PQ is parallel to CD or vice-versa.

Question 3

Which is the easiest and most accurate method to copy a given line segment AB?

A.

Tracing it using a transparent paper

B.

Using a ruler

C.

Using a compass and ruler

D.

Using a set square of (30∘−60∘−90∘)

SOLUTION

Solution : C

Tracing the line may not give accurate result. Similarly, measuring using a ruler may give wrong results depending upon the angle of viewing. Using a compass and a ruler would be the easiest and most accurate method to copy a given line segment AB.

Question 4

Which of the following is an example of perpendicular lines?

1. Corners of your circular room floor.

2. One of the angles in both the set squares of geometry box.

3. Angle included between the hour hand and minute hand when it is 12:15 in your wall clock.

A. 1
B. 2
C. 2 and 3
D. 1 and 3

SOLUTION

Solution : B

There are no corners in a circular floor!

The 2 set squares that you have are both right angled triangles. So, one of the angles is 90∘.

When it is 12:15, the angle included between the hour hand and the minute hand is not 90∘, it is slightly lesser than that because the hour hand moves in clockwise direction as well along with the minute hand.

Question 5

Draw a line AB. At A, draw an arc of length 3cm using compass such that it intersects AB at O. With the same spread of compass, put the compass pointer at O and make an arc that intersects the previous arc at P. With the same spread again, put the compass pointer at P and draw an arc that intersects the first arc at Q. Join A and Q. Using the protractor, measure ∠QAB. What is the value of ∠QAB.

A.

30∘

B.

60∘

C.

90∘

D.

120∘

SOLUTION

Solution : D

If you follow all the steps, you would get this:

If you measure ∠QAB, the value which you would get is 120∘

Question 6

If you have two 30∘- 60∘ - 90∘ set squares, which of the following shapes is impossible to get using them?

A.

Parallelogram

B.

Pentagon

C.

Rhombus

D.

Rectangle

SOLUTION

Solution : C

You know that a rectangle is a parallelogram. In the figures below, we can see that we can make rectangles and also a parallelograms. Also we can make a pentagon. But making a rhombus is impossible by using 2 set squares having 30∘- 60∘ - 90∘ angles.

  

Question 7

Using which of the following, it is not possible to construct a 60∘ angle?

A.

Protractor, Ruler

B.

Compass, Ruler

C.

Set Square (30∘-60∘-90∘)

D.

Set Square (45∘-45∘-90∘)

SOLUTION

Solution : D

We can't draw a 60∘ angle using a set square that has 45∘-45∘-90∘ angles. Using a protractor and compass, and by using a  Set Square (30∘-60∘-90∘), we can draw 60∘ angle.

Question 8

If number of ends in a line is 'X' and the number of ends in a line segment is 'Y', what is the value of 'Y−X'?


__

SOLUTION

Solution :

Number of ends in a line  = 0 = X

Number of ends in a line segment = 2 = Y

Y−X=2−0=2

Question 9

Draw a circle. Now draw any of its two diameters and mark them AC and BD. Join the points A, B, C and D. If ABCD is a square, the diameters must be ___ to each other.

SOLUTION

Solution :

If you draw any of the diameters and join the ends you will always get a rectangle as shown below in figure 1.

Figure 1


Figure 2

Question 10

It is possible to construct an angle equal to 7.5∘ using compass and ruler.

A.

True

B.

False

SOLUTION

Solution : A

It is possible to construct an angle equal to 7.5∘ using compass and ruler.
Steps to draw are:

·Draw an angle of 60∘ using compass and ruler.

·Bisect it to get 30∘.

·Bisect it to get 15∘.

·Bisect it to get 7.5∘.
So we can construct an angle of 7.5∘.

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