Practical Geometry Test

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Practical Geometry Test - 4

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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.
Hence, option (1) is correct.
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.
Hence, option (3) is correct.
Question 3
1 / -0

Let O be a point on the circle and A be a point in the exterior of the circle. Also, let the length of line OA be 9 cm and radius of the circle be 5 cm. What will be the length of line BA, if B is the centre?

A
5 cm

B
7 cm

C
14 cm

D
15 cm

Solution

OA = 9 cm
Radius = 5 cm
So, BX = OB = 5 cm
OB + OA = 5 + 9 = 14 cm
Hence, option (3) is correct.
Question 4
1 / -0

Directions: Read the information given carefully and answer the question that follows.

A perpendicular is drawn to a line segment LK at K using a protractor and point O is marked on the perpendicular, then

A
LK KO

B
LO KO

C
LK KO

D
LO KO

Solution

LK is perpendicular to KO.
Hence, option (3) is correct.
Question 5
1 / -0

Andy constructed an angle of 60° and trisected it. Measure of two angles taken together will be

A
45°

B
30°

C
40°

D
50°

Solution

To trisect is to divide the angle into three parts.
So, when Andy constructed an angle of 60° and trisected it, that means
After that, two angles taken together are 20 + 20 = 40°

Hence, option (3) is correct.
Question 6
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.
Hence, option (2) is correct.
Question 7
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.
Hence, option (4) is correct.
Question 8
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 9
1 / -0

Directions: Choose the correct codes to fill in the blanks.

(I) Perpendicular bisector of a line segment divides the line into ____P____ equal parts.
(II) If OY is the perpendicular bisector of a line segment XZ and it meets XZ at point Y, the XY is equal to ___Q___.
(III) When we trisect a 120° angle, one part is equal to ____R____.

A
A

B
B

C
C

D
D

Solution

(I) We know that the perpendicular bisector of a line segment is the line which is perpendicular to a given line segment and which divides it into two equal line segments.

(II) If OY is the perpendicular bisector of a line segment XZ and it meets XZ at point Y, the XY is equal to YZ.

(III) When we trisect a 120 degree angle, one part is equal to 40 degrees because
So, P - 2, Q - YZ and R - 40°

Hence, option (2) is correct.
Question 10
1 / -0

A line segment AB = 4.6 cm. If it is bisected at P, then find the length of AP.

A
3.5 cm

B
2.8 cm

C
2.6 cm

D
2.3 cm

Solution

Bisect a line means dividing the line segment into two equal parts.

Length of AP = cm = 2.3 cm

Hence, option (4) is correct.
Question 11
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^o, 45^o, 45^o
2nd type of set square has angles - 90^o, 60^o, 30^o
Hence, 120^o is not an angle of set squares.
Question 12
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 13
1 / -0

Directions: 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 Qand 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 Pand 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 14
1 / -0

Directions: 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.

Hence, option (4) is correct.
Question 15
1 / -0

Directions: 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.
Hence, option (4) is correct.