# Free Practical Geometry 03 Practice Test - 6th grade

### Question 1

45∘ angle is drawn. The value of its supplementary angle is _____.

45∘

205∘

135∘

90∘

#### SOLUTION

Solution :C

Two angles are called supplementary angles when they add up to 180∘.

Therefore, the supplementary angle of 45∘ is, 180∘−45∘=135∘

### Question 2

Have you seen long highway roads that never meet and are the same distance apart everywhere? What would such roads be called, in mathematical terms?

Parallel

Intersecting

Oblique

Perpendicular

#### SOLUTION

Solution :A

Parallel lines are two lines that are always the same distance apart and never touch. In order for two lines to be parallel, they must be drawn in the same plane, a perfectly flat surface like a wall or sheet of paper, and they must always be at the same distance.

### Question 3

Choose the option that represent parallel lines?

A book

A cricket ball

A railway track

An ice-cream cone

#### SOLUTION

Solution :C

Sometimes it is helpful to think of parallel lines as a set of railroad tracks. The two sides of the track are created for the wheels on each side of the train to travel along. Because the wheels of the train are always the same distance apart - they do not get closer as they run - the tracks have to be the same distance apart everywhere.In reality, railroad tracks are almost parallel.

### Question 4

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

CD is parallel to PQ

CD is perpendicular to PQ

Both A & B

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 5

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

Tracing it using a transparent paper

Using a ruler

Using a compass and ruler

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 PQ.

### Question 6

Which of the following is an example of perpendicular lines?

1. Corners of your circular room floor

2. One of the angles in both your set squares

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

1

2

2 and 3

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 too as the minute hand moves.

### Question 7

At what time shown in the options, the hour hand and the minute hand of your clock will be perpendicular to each other?

09:00

06:15

03:30

11:00

#### SOLUTION

Solution :A

At 09:00, hour hand and minute hand are at right angles to each other. At all the other instances, the minute hand has moved, so the hour hand would have moved too. Hence, the angle formed will not be 90∘ in those cases.

### Question 8

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 measure of ∠QAB ?

45∘

60∘

75∘

120∘

#### SOLUTION

Solution :D

Following all the steps mentioned, we obtain the following

On measuring ∠QAB, we would get the measure of the angle equal to 120∘.

### Question 9

If ∠XYZ = 90∘, ∠XYZ is also known as a/an

#### SOLUTION

Solution :∠XYZ is also known as a right angle if it is equal to 90∘.

### Question 10

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. Join A and P. Using the protractor, measure ∠PAB. What is the value of ∠PAB.

45∘

30∘

60∘

75∘

#### SOLUTION

Solution :C

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

If you measure ∠PAB, the value which you would get is 60∘.