Practical Geometry Test

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Practical Geometry Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

Each of the four angles at $$J$$ are $$90^\circ$$ and $$PJ=JQ$$. Therefore $$AB$$ is _____ to $$PQ$$.

A
parallel

B
sector

C
perpendicular

D
diagonal

Solution

Each of the four angles at $$J$$ are $$90^\circ$$. Therefore $$AB$$ is perpendicular to $$PQ$$.
Question 2
1 / -0

A perpendicular is to be drawn to a line segment of length $$5$$ cm at a distance of $$3$$ cm from the left end. In what ratio, does it divide the given line?

A
$$3:2$$

B
$$2:3$$

C
$$1:2$$

D
$$1:1$$
Question 3
1 / -0

How many angle bisectors need to be drawn in the steps of construction of an angle $$60^\circ$$?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution
Question 4
1 / -0

You are asked to "construct" an angle of $$90^\circ$$. Which of the following methods is considered appropriate for construction

A
Using a compass and straightedge, copy an angle that appears to be close to $$90^\circ$$ from a diagram in your textbook.

B
Using a compass and straightedge, construct two parallel lines and label on of the angles $$90^\circ$$.

C
Using a compass and straightedge, construct angles of $$60^\circ$$ and $$120^\circ$$ and bisect the angle between them.

D
Using a protractor, draw an angle of $$90^\circ$$

Solution

An angle is drawn most appropriate using a compass.
Now bisector of $$60^{\circ}$$ and $$120^{\circ}$$ gives an angle of $$90^{\circ}$$
So option $$C$$ is correct.
It can also be drawn using protractor but less accurate then compass.
Question 5
1 / -0

How many angle bisectors need to be drawn in the steps of construction of an angle $$45^\circ$$?

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution

Steps for construction:
$$1)$$ Construct a perpendicular line.
$$2)$$ Place a compass on a intersection line.
$$3)$$ Adjust compass width to reach start point
$$4)$$ Draw an arc that intersects perpendicular line.
$$5)$$ Place a ruler on a start point and where arc intersects perpendicular line.
$$6)$$ Draw a 45 degree line
So only $$1$$ angle bisector is need to be drawn in the steps of construction of an angle $$45^o$$
Question 6
1 / -0

Directions For Questions

The following are the jumbled steps to construct a perpendicular from a point $$P$$ on line $$AB$$. $$(P$$ lies on line $$AB)$$.
1. From points $$C$$ and $$D$$, mark two intersecting arcs on either side of the line $$AB$$. Name the intersection point as $$E$$.
2. From point $$P$$, mark two equidistant points from $$P$$ on line $$AB$$, and name them as $$C$$ and $$D$$.
3. Join $$E$$ and $$P$$. $$EP$$ is the required perpendicular.
4. Draw segment $$AB$$ and take any point $$P$$ on it.

...view full instructions

The third step in the process will be:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Correct sequence of steps is :
Step 1: Draw segment $$AB$$ and take a point $$P$$ on it.
Step 2: From point $$P$$, mark two equidistant points from $$P$$ on line $$AB$$, and name them $$C$$ and $$D$$
Step 3 : From points $$C$$ and $$D$$ mark two intersecting arcs on either side of the line $$AB$$.Name the intersection point as $$E$$
Step 4: Join $$E$$ and $$P$$. $$EP$$ is the required perpendicular.
So the third step is $$!$$
So option $$A$$ is correct.
Question 7
1 / -0

Directions For Questions

The steps for constructing a perpendicular from point $$A$$ to line $$PQ$$ is given in jumbled order as follows: $$(A$$ does not lie on $$PQ)$$
1. Join $$R-S$$ passing through $$A$$.
2. Place the pointed end of the compass on $$A$$ and with an arbitrary radius, mark two points $$D$$ and $$E$$ on line $$PQ$$ with the same radius.
3. From points $$D$$ and $$E$$, mark two intersecting arcs on either side of $$PQ$$ and name them $$R$$ and $$S$$.
4. Draw a line $$PQ$$ and take a point $$A$$ anywhere outside the line.

...view full instructions

The third step in the process is:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Correct sequence is :

Step 1 . Draw a line $$PQ$$ and take a point $$A$$ anywhere outside the line.

Step 2. Place the pointed end of the compass on $$A$$ and with an arbitrary radius, mark two points $$D$$ and $$E$$ on line $$PQ$$ with the same radius.

Step 3. From points $$D$$ and $$E$$, mark two intersecting arcs on either side of $$PQ$$ and name them $$R$$ and $$S.$$

Step 4. Join $$R−S$$ passing through $$A$$.

So the third step is $$3$$.
Question 8
1 / -0

Directions For Questions

The steps for constructing a perpendicular from point $$A$$ to line $$PQ$$ is given in jumbled order as follows: $$(A$$ does not lie on $$PQ)$$
1. Join $$R-S$$ passing through $$A$$.
2. Place the pointed end of the compass on $$A$$ and with an arbitrary radius, mark two points $$D$$ and $$E$$ on line $$PQ$$ with the same radius.
3. From points $$D$$ and $$E$$, mark two intersecting arcs on either side of $$PQ$$ and name them $$R$$ and $$S$$.
4. Draw a line $$PQ$$ and take a point $$A$$ anywhere outside the line.

...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 line $$PQ$$ and take a point $$A$$ anywhere outside the line.

Step 2. Place the pointed end of the compass on $$A$$ and with an arbitrary radius, mark two points $$D$$ and $$E$$ on line $$PQ$$ with the same radius.

Step 3. From points $$D$$ and $$E$$, mark two intersecting arcs on either side of $$PQ$$ and name them $$R$$ and $$S.$$

Step 4. Join $$R−S$$ passing through $$A$$.

So the first step is $$4$$

Option $$D$$ is correct.
Question 9
1 / -0

The steps for constructing a perpendicular from point $$A$$ to line $$PQ$$ is given in jumbled order as follows: $$(A$$ does not lie on $$PQ)$$
1. Join $$R-S$$ passing through $$A$$.
2. Place the pointed end of the compass on $$A$$ and with an arbitrary radius, mark two points $$D$$ and $$E$$ on line $$PQ$$ with the same radius.
3. From points $$D$$ and $$E$$, mark two intersecting arcs on either side of $$PQ$$ and name them $$R$$ and $$S$$.
4. Draw a line $$PQ$$ and take a point $$A$$ anywhere outside the line.
The second step in the process is:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Correct sequence is :

Step 1 . Draw a line $$PQ$$ and take a point $$A$$ anywhere outside the line.

Step 2. Place the pointed end of the compass on $$A$$ and with an arbitrary radius, mark two points $$D$$ and $$E$$ on line $$PQ$$ with the same radius.

Step 3. From points $$D$$ and $$E$$, mark two intersecting arcs on either side of $$PQ$$ and name them $$R$$ and $$S.$$

Step 4. Join $$R−S$$ passing through $$A$$.

So the second step is $$2$$.

Option $$B$$ is correct.
Question 10
1 / -0

In square $$\square ABCD$$, join $$AC$$. Let $$O$$ be midpoint of $$AC$$ and $$AO \perp BD$$.
Which one of following is true?

A
$$AO$$ passes through $$D$$.

B
$$AO$$ cuts $$CD$$ between $$C,D$$

C
$$AO$$ cuts $$BC $$ in point other than $$B,C$$.

D
$$AO$$ passes through $$C$$.

Solution

According to property of square, diagonals bisect each other at right angle.
Since, AO is perpendicular to BD and O is midpoint of AC. So, AO must pass through point C.
Hence, Option D is correct.

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Re-Attempt Weekly Quiz Competition

Practical Geometry Test - 9

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Practical Geometry Test - 9

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SHARING IS CARING

Question 1

parallel

sector

perpendicular

diagonal

Solution

Question 2

$$3:2$$

$$2:3$$

$$1:2$$

$$1:1$$

Question 3

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 4

Using a compass and straightedge, copy an angle that appears to be close to $$90^\circ$$ from a diagram in your textbook.

Using a compass and straightedge, construct two parallel lines and label on of the angles $$90^\circ$$.

Using a compass and straightedge, construct angles of $$60^\circ$$ and $$120^\circ$$ and bisect the angle between them.

Using a protractor, draw an angle of $$90^\circ$$

Solution

Question 5

$$0$$

$$1$$

$$2$$

$$3$$

Solution

Question 6

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 7

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 8

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 9

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 10

$$AO$$ passes through $$D$$.

$$AO$$ cuts $$CD$$ between $$C,D$$

$$AO$$ cuts $$BC $$ in point other than $$B,C$$.

$$AO$$ passes through $$C$$.

Solution

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