Practical Geometry Test

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Practical Geometry Test - 4

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Question 1
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Directions For Questions

The steps for construction of an $$\angle ABC$$ of measure $$60^\circ$$ is given below in jumbled order:
1. Join $$B-E$$ and extend it as a ray $$BA$$.
2. Draw a ray $$BC$$.
3. With the same radius and the pointed end of the compass at $$D$$, mark a point $$E$$ on the same arc.
4. With the pointed end of the compass at $$B$$ and any arbitrary radius, draw an arc and mark the intersection point with ray $$BC$$ as $$D$$.

...view full instructions

The first step in the process is:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Correct sequence is :

Step 1. Draw a ray $$BC$$.

Step 2. With the pointed end of the compass at B and any arbitrary radius, draw an arc and mark the intersection point with ray $$BC$$ as $$D.$$

Step 3. With the same radius and the pointed end of the compass at $$D$$, mark a point $$E$$ on the same arc.

Step 4 Join $$B−E$$ and extend it as a ray $$BA.$$

So the first step is $$2$$

Option $$B$$ is correct.
Question 2
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Which of the following lines from point $$P$$ is a perpendicular to line $$AB$$?

A
$$PQ$$

B
$$PR$$

C
$$PS$$

D
$$PT$$

Solution

Line $$PR$$ makes a right angle with line $$AB$$
$$\therefore PR$$ is perpendicular to $$AB$$
Option $$B$$ is correct.
Question 3
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Each angle of equilateral triangle is $$ 60^\circ$$. The angles are bisected then each angle will be of:

A
$$60^o$$

B
$$30^o$$

C
$$90^o$$

D
$$120^o$$

Solution

Angle bisector divide the angle in two equal parts.
$$\therefore $$ bisected angle $$=\dfrac{60^{\circ}}{2}=30^{\circ}$$
So option $$B$$ is correct.
Question 4
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A square is given and an angle of $$30^{o}$$ is drawn from one of its vertex . The figure will look like what?

A

B

C

D

Solution

Place a protractor and draw an angle of $$30^{\circ}$$ on one of its vertex.
If angle is drawn on the topmost right vertex then the figure looks like figure in option $$D$$
So option $$D$$ is correct.
Question 5
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Directions For Questions

The steps for constructing an $$\angle ABC$$ of measure $$120^\circ$$ are given below in jumbled order:
1. From the point $$E$$, mark a point $$F$$ on the same arc with the same radius.
2. Place the pointed end of the compass on $$B$$ and draw a semi-circular arc with arbitrary radius and name its intersection with ray $$BC$$ as $$D$$.
3. Draw a ray $$BC$$.
4. From point $$D$$, mark a point $$E$$ on the arc with the same radius.
5. Join $$B-F$$ and extend it to obtain ray $$BA$$

...view full instructions

The fourth step in the process is:

A
$$1$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

Correct sequence is :
Step 1. Draw a ray $$BC$$.
Step 2.Place the pointed end of the compass on $$B$$ and draw a semi-circular arc with arbitrary radius and name its intersection with the ray $$BC$$ as $$D$$.
Step 3. From $$D$$ mark a point $$E$$ on the arc with the same radius.
Step 4. From point $$E$$, mark a point $$F$$ on the same arc with same radius.
Step 5. Join $$B-F$$ and extend it to obtain ray $$BA$$
So the fourth step is $$1$$
Option $$A$$ is correct.
Question 6
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The steps of construction of an $$\angle AOB=45^{o}$$ is given in jumbled order below:
1. Place compass on intersection point.
2. Place ruler on start point and where arc intersects perpendicular line.
3. Adjust compass width to reach start point.
4. Construct a perpendicular line.
5. Draw $$45$$ degree line.
6. Draw an arc that intersects perpendicular line.
Which step comes first?

A
$$1$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

Correct sequence is :
1. Construct a perpendicular line .
2. Draw an arc that intersect the perpendicular line.
3. Adjust the compass width to reach the start point .
4.Place compass on intersection point.
5. Place ruler on start point and where the arc intersects the perpendicular line.
6. Draw $$45$$ degree line.
So the first step is $$4$$
Option $$C$$ is correct.
Question 7
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An architect needs a staircase attached to a wall.The angle between stair and ground needs to be 30.
His plan will look like:

A

B

C

D

Solution

Only option $$(B)$$ shape have an angle equivalent to $$30^o$$.
So architect plan will look like shape $$(B)$$.
Question 8
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The steps for constructing an $$\angle ABC$$ of measure $$120^\circ$$ are given below in jumbled order:
1. From the point $$R$$, mark a point $$P$$ on the same arc with the same radius.
2. Place the pointed end of the compass on $$B$$ and draw a semi-circular arc with arbitrary radius and name its intersection with ray $$BC$$ as $$Q$$.
3. Draw a ray $$BC$$.
4. From point $$Q$$, mark a point $$R$$ on the arc with the same radius.
5. Join $$B-P$$ and extend it to obtain ray $$BA$$

$$The \ fifth \ step \ in \ the \ process \ is:$$

A
$$2$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

Correct sequence is :
Step 1. Draw a ray $$BC$$.
Step 2.Place the pointed end of the compass on $$B$$ and draw a semi-circular arc with arbitrary radius and name its intersection with the ray $$BC$$ as $$Q$$.
Step 3. From $$Q$$ mark a point $$R$$ on the arc with the same radius.
Step 4. From point $$R$$, mark a point $$P$$ on the same arc with same radius.
Step 5. Join $$B-P$$ and extend it to obtain ray $$BA$$

So the fifth step is $$5$$
Option $$D$$ is correct.
Question 9
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Directions For Questions

The steps for constructing an $$\angle ABC$$ of measure $$120^\circ$$ are given below in jumbled order:
1. From the point $$E$$, mark a point $$F$$ on the same arc with the same radius.
2. Place the pointed end of the compass on $$B$$ and draw a semi-circular arc with arbitrary radius and name its intersection with ray $$BC$$ as $$D$$.
3. Draw a ray $$BC$$.
4. From point $$D$$, mark a point $$E$$ on the arc with the same radius.
5. Join $$B-F$$ and extend it to obtain ray $$BA$$

...view full instructions

The second step in the process is:

A
$$1$$

B
$$2$$

C
$$4$$

D
$$5$$

Solution

Correct sequence is :
Step 1. Draw a ray $$BC$$.
Step 2.Place the pointed end of the compass on $$B$$ and draw a semi-circular arc with arbitrary radius and name its intersection with the ray $$BC$$ as $$D$$.
Step 3. From $$D$$ mark a point $$E$$ on the arc with the same radius.
Step 4. From point $$E$$, mark a point $$F$$ on the same arc with same radius.
Step 5. Join $$B-F$$ and extend it to obtain ray $$BA$$
So the second step is $$2$$
Option $$B$$ is correct.
Question 10
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Which of the following angles cannot be constructed using a protractor?

A
$$94.3^{o}$$

B
$$56^{o}$$

C
$$75^{o}$$

D
$$90^{o}$$

Solution

A protractor has integral marking of angles .

So $$56^{\circ}$$ , $$75^{\circ}$$ , $$90^{\circ} $$ can be drawn easily by protractor as they are integers .

$$94.3^{\circ}$$ can not be drawn , it has decimal part.