Practical Geometry Test

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Practical Geometry Test - 2

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Question 1
1 / -0

How many lines can pass through two given points?

A
1

B
2

C
3

D
Infinite

Solution

Only one line can pass through two points.
Infinite number of lines can pass through one point.
Question 2
1 / -0

Which of the following angles are drawn, if an angle of 60º is bisected using a compass and a ruler?

A
0º and 60º

B
15º and 45°

C
30° and 30°

D
45° and 15º

Solution

Bisection is the division of a given quantity in two equal parts.
60º divided by 2 is equal to 30º.
Question 3
1 / -0

How many angle bisector(s) can an angle have?

A
0

B
1

C
2

D
Infinite

Solution

An angle bisector is a line that divides any angle into two equal halves. Since, an angle can be divide in two equal halves only once.
Therefore, every angle has 1 angle bisector.
Question 4
1 / -0

If there is an isosceles triangle ABC and AB = AC, then find the number of perpendicular bisector(s) for the unequal line segment.

A
Three

B
Four

C
Two

D
One

Solution

The number of perpendicular bisector for an unequal line segment in an isosceles triangle is one because that perpendicular bisector will divide the unequal line segments into two equal parts.
Question 5
1 / -0

To draw an angle of 135° using a pair of compass and ruler, bisect the angle between

A
90° and 150°.

B
90° and 180°

C
0° and 180°

D
120° and 180°

Solution

To draw an angle of 135° using a pair of compass and ruler, bisect the angle between 90° and 180°.
Question 6
1 / -0

Which of the following angles is not an angle of set squares?

A
30°

B
45°

C
90°

D
120°

Solution

There are 2 types of set squares.
1st type of set square has angles - 90°, 45°, 45°

2nd type of set square has angles - 90°, 60°, 30°
Hence, 120° is not an angle of set squares.
Question 7
1 / -0

Which of the following steps is INCORRECT while constructing the angle of 45°?

A
Draw a line PQ, to be one leg of the angle.

B
Set the compass on P and the width to just over half of PQ. From P and Q, draw intersecting arcs above and below PQ.

C
Draw a straight line between two arcs of intersection and mark O as the midpoint where the straight line intersects PQ. From the midpoint of PQ, set the compass width to P and draw an arc across the perpendicular creating a point C.

D
Draw a line PR through the point Q; the angle ROQ has the measure of 45 degrees.

Solution

Step 4 is incorrect. It should be as: Draw a line PR through the point C; the angle RPQ has the measure of 45 degrees.
Question 8
1 / -0

Arrange the given steps in the correct order of constructing a 60° angle using a ruler and a compass.

1. Place the point of the compass at Q and draw an arc that passes through P. Let this arc cut the arc drawn in previous step at R.
2. Join P to R. The angle RPQ is 60°.
3. Place the point of the compass at P and draw an arc that passes through line PQ.
4. Draw the arm PQ.

A
2, 4, 1, 3

B
4, 3, 1, 2

C
1, 4, 2, 3

D
4, 1, 2, 3

Solution

The correct sequence of the steps would be as follows.

Step 4. Draw the arm PQ.
Step 3. Place the point of the compass at P and draw an arc that passes through line PQ.

Step 1. Place the point of the compass at Q and draw an arc that passes through P. Let this arc cut the arc drawn in previous step at R.
Step 2. Join P to R. The angle RPQ is 60°.
Question 9
1 / -0

Read the given statements carefully and choose the correct option.

(Note: T = True and F = False)

(i) Two different points on the boundary of a circle will have different distances from the center of that circle.
(ii) If we bisect the angle of a rectangle, then we get two angles of 45°.
(iii) A line has infinite length.

A
F, F, F

B
T, F, T

C
F, F, T

D
F, T, T

Solution

(i) Every point on a circle is at equal distance from its center. This means that two different points on the boundary of a circle will be at equal distances from its center.
Hence, statement (i) is false.

(ii) Rectangle has four 90° angles and if we bisect an angle of rectangle, it would be 45°. (True)

(iii) A line has infinite length. (True)

F, T, T is the correct order.
Question 10
1 / -0

Read the statements carefully and choose the correct option.

Statement 1: Through a line in a plane, number of lines that can be drawn is 2.
Statement 2: The angle bisector of 180° will bisect it into two angles of 100° and 80°.

A
Both statements 1 and 2 are true.

B
Statement 1 is true, but statement 2 is false.

C
Statement 1 is false, but statement 2 is true.

D
Neither statement 1 nor statement 2 is true.

Solution

Statement 1 is false because through a line in a plane, number of lines that can be drawn is infinite.

Statement 2 is false because the angle bisector of 180° will bisect it into two angles of 90° each.

Therefore, neither statement 1 nor statement 2 is true.

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Practical Geometry Test - 2

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Practical Geometry Test - 2

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Question 1

1

2

3

Infinite

Solution

Question 2

0º and 60º

15º and 45°

30° and 30°

45° and 15º

Solution

Question 3

0

1

2

Infinite

Solution

Question 4

Three

Four

Two

One

Solution

Question 5

90° and 150°.

90° and 180°

0° and 180°

120° and 180°

Solution

Question 6

30°

45°

90°

120°

Solution

Question 7

Draw a line PQ, to be one leg of the angle.

Set the compass on P and the width to just over half of PQ. From P and Q, draw intersecting arcs above and below PQ.

Draw a straight line between two arcs of intersection and mark O as the midpoint where the straight line intersects PQ. From the midpoint of PQ, set the compass width to P and draw an arc across the perpendicular creating a point C.

Draw a line PR through the point Q; the angle ROQ has the measure of 45 degrees.

Solution

Question 8

2, 4, 1, 3

4, 3, 1, 2

1, 4, 2, 3

4, 1, 2, 3

Solution

Question 9

F, F, F

T, F, T

F, F, T

F, T, T

Solution

Question 10

Both statements 1 and 2 are true.

Statement 1 is true, but statement 2 is false.

Statement 1 is false, but statement 2 is true.

Neither statement 1 nor statement 2 is true.

Solution

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