Practical Geometry Test

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Practical Geometry Test - 3

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Question 1
1 / -0

A line is drawn randomly in a plane. How many lines can be drawn parallel to this line that are lying in the same plane?

A
Infinite

B
1

C
0

D
2

Solution

As seen in the picture above, a line is drawn and infinite such lines can be drawn parallel to it.
Question 2
1 / -0

An angle 135^ois drawn using a compass and ruler by bisecting _________.

A
90^o and 150^o

B
120^oand 180^o

C
150^o

D
90^oand 180^o

Solution

In the above figure,
1. A 180^o angle is constructed on on line AB.
1. A 90^o angle is constructed from 180^o angle.
2. A 45^o angle is formed from this perpendicular because
90^o+ 45^o= 135^o
Hence, angle 135^ois drawn using a compass and ruler by bisecting 90^o and 180^o.
Question 3
1 / -0

In the given figure, the distance between O and G is 8.5 cm. If the radius of the given circle is 3.5 cm, find the length of BG.

A
3.5 cm

B
4 cm

C
5 cm

D
6 cm

Solution

BG = OG - OB (radius) = 8.5 - 3.5 = 5 cm
Question 4
1 / -0

Two lines AB and PM intersect at a point O and the angle formed at O is 90^o.

Which of the following relationships is/are true?
1. PM ⊥ AB
2. AB || PO

A
Only 1

B
Only 2

C
Both 1 and 2

D
None of the statements

Solution

Form the above diagram, it can be seen that PM ⊥ AB.
Question 5
1 / -0

Megan draws an angle of 175^o, and Garvin divides it into five equal parts. What will be the measure of two angles taken together?

A
35^o

B
70^o

C
85^o

D
90^o

Solution

If we divide 175^o into five equal parts, each part will be equal to 175^o ÷ 5 = 35^o.
So, the measure of two angles taken together will be 70^o.
Question 6
1 / -0

A circle has ___________ end points.

A
0

B
1

C
2

D
infinite

Solution

Acircle is a closed figure, so it has no end points.
Question 7
1 / -0

The total number of angle bisectors possible for a given angle is

A
infinite

B
2

C
0

D
1

Solution

It can be seen that there is only one angle bisector.
The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts.
Question 8
1 / -0

Alex wants to draw an angle of 165^o using a compass and ruler. Which of the following pairs of angles should he use in order to draw it successfully?

A
90^o and 180^o

B
0^o and 180^o

C
150^o and 180^o

D
90^oand60^o

Solution

150^o+ 15^o= 165^o
Question 9
1 / -0

A line segment AB is trisected and hence new points, that is, P and Q are introduced on the line. Assuming P to be in between A and Q, find the length of AQ if the length of AB is 9.3 cm.

A
6.1 cm

B
6.2 cm

C
3.1 cm

D
4.1 cm

Solution

Since AB is trisected, the value each part is 9.3 ÷ 3 = 3.1 cm.
AQ = 3.1 + 3.1 = 6.2 cm
Question 10
1 / -0

What is the purpose of a set square?

A
To draw lines at specific angles such as 90°, 45°, 60°, or 30°

B
To draw a square only

C
To measure any angle

D
None of these

Solution

A set square is a right-angled triangular plate for drawing lines, especially at 90°, 45°, 60°, or 30°.
Question 11
1 / -0

Following are the steps to construct 30^o. Find the incorrect step(s) here.

Step 1: Draw the arm PQ.
Step 2: Place the point of the compass at P and draw an arc that passes through Q.
Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.
Step 4: With the point of the compass still at Q, draw an arc (point T).
Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.
Step 6: Join T and P. The angle QPT is 30^o.

A
None of these

B
Step 1

C
Step 2

D
Steps 3 and 4

Solution

Step 1: Draw the arm PQ.
Step 2: Place the point of the compass at P and draw an arc that passes through Q.
Step 3: Place the point of the compass at Q and draw an arc that cuts the arc drawn in Step 2 at R.
Step 4: With the point of the compass still at Q, draw an arc near T as shown.
Step 5: With the point of the compass at R, draw an arc to cut the arc drawn in Step 4 at T.
Step 6: Join T and P. The angle QPT is 30Âº.

Question 12

1 / -0

Fill in the blanks:

A P is a special kind of segment, ray, or line that intersects a given segment at a Q angle, and passes through the given segment's R .

	P	Q	R
A	perpendicular bisector	90°	midpoint
B	midpoint	90°	perpendicular bisector
C	bisector	90°	midpoint
D	perpendicular bisector	90°	bisects

D

C

B

A

Solution

A perpendicular bisector is a special kind of segment, ray, or line that intersects a given segment at a 90° angle, and passes through the given segment's midpoint.

Question 13
1 / -0

Arrange the following steps in the order to draw an angle bisector of a given angle.

1. With 'B' as centre, draw an arc of same radius to cut the previous arc at 'C'.
2. With 'A' as centre, draw an arc of radius more than half of AB, in the interior of the given angle.
3. With 'O' as centre, draw an arc of any radius to cut the rays of the angle at A and B.
4. Join OC. OC is the angle bisector of the given angle.
5. Construct an angle of the given measure at O using a protractor.

A
25134

B
25413

C
53214

D
54321

Solution

Following is the correct arrangement for given steps -
5 : Construct an angle of the given measure at O using a protractor.
3 : With 'O' as centre, draw an arc of any radius to cut the rays of the angle at A and B.
2 : With 'A' as centre, draw an arc of radius more than half of AB, in the interior of the given angle.
1 : With 'B' as centre, draw an arc of same radius to cut the previous arc at 'C'.
4 : Join OC. OC is the angle bisector of the given angle.

Therefore, correct arrangement will be 53214.

Question 14

1 / -0

State T for True and F for False.

1. With a given centre, infinite circles can be drawn.
2. A single line can act as a perpendicular for two parallel lines.
3. Diagonal of a square acts like its angle bisector.

	1	2	3
A	F	F	T
B	T	F	T
C	F	F	T
D	T	T	T

A

D

B

C

Solution

With a given centre, infinite circles can be drawn.

A single line can act as a perpendicular for two parallel lines.

Diagonal of a square acts like its angle bisector.

Question 15
1 / -0

Read the following statements carefully and choose the correct option.

Statement-1: A line which bisects a given line making an angle of 90^o at the point of intersection is called perpendicular bisector.
Statement-2: The angle of 60^o can be constructed using a compass and ruler.

A
Both statements are true.

B
Only 1 is true.

C
Only 2 is true.

D
Both are false.

Solution

Both the given statements are true and are facts.

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Practical Geometry Test - 3

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Practical Geometry Test - 3

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Question 1

Infinite

1

0

2

Solution

Question 2

90o and 150o

120o and 180o

150o

90o and 180o

Solution

Question 3

3.5 cm

4 cm

5 cm

6 cm

Solution

Question 4

Only 1

Only 2

Both 1 and 2

None of the statements

Solution

Question 5

35o

70o

85o

90o

Solution

Question 6

0

1

2

infinite

Solution

Question 7

infinite

2

0

1

Solution

Question 8

90o and 180o

0o and 180o

150o and 180o

90o and 60o

Solution

Question 9

6.1 cm

6.2 cm

3.1 cm

4.1 cm

Solution

Question 10

To draw lines at specific angles such as 90°, 45°, 60°, or 30°

To draw a square only

To measure any angle

None of these

Solution

Question 11

None of these

Step 1

Step 2

Steps 3 and 4

Solution

Question 12

D

C

B

A

Solution

90^o and 150^o

120^oand 180^o

150^o

90^oand 180^o

35^o

70^o

85^o

90^o

90^o and 180^o

0^o and 180^o

150^o and 180^o

90^oand60^o