Practical Geometry Test

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Practical Geometry Test - 3

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Question 1
1 / -0

While constructing a parallel line to a given line, we______.

A
copy a segment

B
bisect a segment

C
copy an angle

D
construct a perpendicular

Solution

To draw a parallel line to a given line $$l$$, we have to just copy the angle $$\angle AOL$$, so that
$$\angle AOL=\angle AEM$$
In this case $$AB$$ act as a transverse and $$\angle AOL$$ and $$\angle AEM$$ are corresponding angles and they are equal if line $$l$$ is parallel to line $$m$$
Question 2
1 / -0

Identify the given lines $$l,\ m$$ are ________.

A
Parallel

B
Perpendicular

C
Bisector

D
Diagonal

Solution

The construction works by using the fact that a transverse line draws across two parallel lines create pairs of equal corresponding angles. It uses this in reverse by creating two equal corresponding angles, it can create the parallel lines.
Question 3
1 / -0

Length of sides of a $$\triangle ABC$$ is $$AB=5\ cm$$, $$AC = 3\ cm$$ and $$BC=4\ cm$$. If the construction of the triangle formed by these three sides include following steps, then answer the following question:
Which of the following is the last step of construction?
Steps of construction:
Step 1. Now join $$A$$ to $$C$$ and $$B$$ to $$C$$.
Step 2. Assuming $$A$$ a centre draw an arc of radius $$3 \ \ cm$$
Step 3. Now assuming $$B$$ as centre draw an arc of $$4 \ \ cm$$ intersecting the previous arc at $$C$$.
Step 4. Draw a line segment $$AB= 5 \ cm$$

A
1

B
2

C
3

D
4

Solution

Steps of construction:
Step 1. Draw a line segment $$AB=5\ \ cm$$
Step 2. Assuming $$A$$ a centre draw an arc of radius $$3 \ \ cm$$
Step 3. Now assuming $$B$$ as centre draw an arc of $$4 \ \ cm$$ intersecting the previous arc at $$C$$.
Step 4. Now join $$A$$ to $$C$$ and $$B$$ to $$C$$.
Hence, (A) will be correct.
Question 4
1 / -0

The steps for construction of $$\triangle DEF$$ with $$DE = 4\ cm, EF=6.5\ cm$$ and $$DF = 8.6\ cm$$ are given below in jumbled order:
1. Draw arcs of length $$4\ cm$$ from $$D$$ and $$6.5\ cm$$ from $$F$$ and mark the intersection point as $$E$$.
2. Join $$D-E$$ and $$F-E$$.
3. Draw a line segment of length $$DF = 8.6\ cm$$.

The correct order of the steps is:

A
$$3-1-2$$

B
$$1-2-3$$

C
$$2-3-1$$

D
$$2-1-3$$

Solution

Correct sequence is
Step 1: Draw a line segment of length $$DF=8.6 cm$$.
Step2 :Draw arcs of length $$4 cm$$ from $$D$$ and $$6.5 cm$$ from $$F$$ and mark the intersection point as $$E$$
Step 3: Join $$D-E$$ and $$F-E$$.
So the sequence is $$3-1-2$$
Question 5
1 / -0

Construct a triangle $$ABC$$, in which $$AB = 5.5 cm, AC = 6.5 cm$$ and $$\angle BAC = 70^{\circ}$$.
If the stpes of construction are given as below the answer the following question:
Which is the 2nd step of construction?
1) At $$A$$, construct a line segment $$AE$$, sufficiently large, such that $$\angle BAC$$ at $$70^\circ$$, use protractor to measure $$70^\circ$$
2) Draw a line segment which is sufficiently long using ruler.
3) With $$A$$ as centre and radius $$6.5cm$$, draw the line cutting $$AE$$ at C, join $$BC$$, then $$ABC$$ is the required triangle.
4) Locate points $$A$$ and $$B$$ on it such that $$AB = 5.5cm$$.

A
1

B
2

C
3

D
none of the above

Solution

Below are the correct steps.
1. Draw a line segment which is sufficiently long using ruler.
2.Locate points $$A$$ and $$B$$ on it such that $$AB=5.5 \ cm$$
3.At $$A$$ construct a line segment $$AE$$ , sufficiently large, such that $$\angle BAC=70^\circ$$, use protractor to measure 70°.
4. With $$A$$ as centre and radius $$6.5 \ cm$$ draw the line cutting $$AE$$ at $$C$$, join $$BC$$ then $$ABC$$ is the required triangle.
Hence, (D) will be correct answer.
Question 6
1 / -0

Given a, b and c are sides of a triangle,identify the correctly constructed triangle.

A

B

C

D
Question 7
1 / -0

Construct a $$\triangle PQR$$ such that $$\angle P = 30^\circ, \angle Q = 60^\circ$$ and $$PQ = 10\ cm$$.
If following are the steps of construction, then answer the following question:
Which of the following is the first step of construction?
Steps of Construction:
Step 1. At $$P$$, draw a ray making an angle of $$30^{\circ}$$.
Step 2. At $$Q$$, draw another ray making an angle of $$60^{\circ}$$ which intersects the first ray at $$R$$. Thus, $$\triangle PQR$$ is the required triangle.
Step 3. Draw a line segment $$PQ = 10\space\mathrm{cm}$$.

A
1

B
2

C
3

D
none of these

Solution

Steps of Construction:
(i) Draw a line segment $$PQ = 10\space\mathrm{cm}$$.
(ii) At $$P$$, draw a ray making an angle of $$30^{\circ}$$.
(iii) At $$Q$$, draw another ray making an angle of $$60^{\circ}$$ which intersects the first ray at $$R$$.
$$\triangle PQR$$ is the required triangle.
Hence, (C) wil be correct answer.
Question 8
1 / -0

Length of sides of a $$\triangle ABC$$ is $$AB=5\ cm$$, $$AC = 3\ cm$$ and $$BC=4\ cm$$. Then, construct the triangle formed by these three sides by following these steps. Put them in proper order.
Step 1. Draw a line segment $$AB=5\ \ cm$$
Step 2. Now assuming $$B$$ as centre draw an arc of $$4 \ \ cm$$ intersecting the previous arc at $$C$$.
Step 3. Assuming $$A$$ a centre draw an arc of radius $$3 \ \ cm$$
Step 4. Now join $$A$$ to $$C$$ and $$B$$ to $$C$$.

A
$$1-3-2-4$$

B
$$1-4-2-3$$

C
$$2-3-4-1$$

D
none of these

Solution

Steps of construction
Step 1. Draw a line segment $$AB=\ \ cm$$
Step 2. Assuming $$A$$ a centre draw an arc of radius $$3 \ \ cm$$
Step 3. Now assuming $$B$$ as centre draw an arc of $$4 \ \ cm$$ intersecting the previous arc at $$C$$.
Step 4. Now join $$A$$ to $$C$$ and $$B$$ to $$C$$.
So $$1-3-2-4$$ is the correct order
Question 9
1 / -0

Construct a $$\triangle PQR$$ such that $$\angle P = 30^\circ, \angle Q = 60^\circ$$ and $$PQ = 10\ cm$$.
If following are the steps of construction, then which of the following is not a part of construction?
Steps of Construction:
(i) Draw a line segment $$PQ = 10\space\mathrm{cm}$$.
(ii) At $$P$$, draw a ray making an angle of $$30^{\circ}$$.
(iii) At $$Q$$, draw another ray making an angle of $$60^{\circ}$$ which intersects the first ray at $$R$$.
$$\triangle PQR$$ is the required triangle.

A
1

B
2

C
3

D
none of these

Solution

Steps of Construction:
(i) Draw a line segment $$PQ = 10\space\mathrm{cm}$$.
(ii) At $$P$$, draw a ray making an angle of $$30^{\circ}$$.
(iii) At $$Q$$, draw another ray making an angle of $$60^{\circ}$$ which intersects the first ray at $$R$$.
$$\triangle PQR$$ is the required triangle.
Hence, (D) wil be correct answer.
Question 10
1 / -0

Construct a $$\triangle PQR$$ such that $$\angle P = 30^\circ, \angle Q = 60^\circ$$ and $$PQ = 10\ cm$$.

If the following are the steps of construction, then answer the following question:

Which of the following is the last step of construction?

Steps of Construction:

Step 1. At $$P$$, draw a ray making an angle of $$30^{\circ}$$.

Step 2. At $$Q$$, draw another ray making an angle of $$60^{\circ}$$
which intersects the first ray at $$R$$.
Thus, $$\triangle PQR$$ is the required triangle.

Step 3. Draw a line segment $$PQ = 10\space\mathrm{cm}$$.

A
1

B
2

C
3

D
none of these

Solution

Steps of Construction:

(i) Draw a line segment $$PQ = 10\space\mathrm{cm}$$.

(ii) At $$P$$, draw a ray making an angle of $$30^{\circ}$$.

(iii) At $$Q$$, draw another ray making an angle of $$60^{\circ}$$ which intersects the first ray at $$R$$.

$$\triangle PQR$$ is the required triangle.

Hence, (B) will be the correct answer.