Practical Geometry Test

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Practical Geometry Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Length of two sides of a $$\triangle ABC$$ is $$AB=6\ cm$$ and $$BC=7\ cm$$. Then, which of the following can represent the third side of the triangle ? Also, construct the triangle formed by these three sides by following these steps. Put them in proper order.
Step 1. Draw a line segment $$AB=6\ \ cm$$
Step 2. Now assuming $$B$$ as centre draw an arc of $$7 \ \ cm$$ intersecting the previous arc at $$C$$.
Step 3. Assuming $$A$$ a centre draw an arc of radius $$8 \ \ cm$$
Step 4. Now join $$A$$ to $$C$$ and $$B$$ to $$C$$.

A
$$8\ cm$$, $$1-3-2-4$$

B
$$13\ cm$$, $$1-3-2-4$$

C
$$14\ cm$$,$$1-2-3-4$$

D
$$15\ cm$$, $$4-3-2-1$$

Solution

A triangle can be formed if sum of any two sides is greater then the third side.
Here $$AB=6$$ cm and $$BC=7$$ cm
Now $$AB+BC>AC$$
$$6+7>AC$$
$$AC<13$$ cm
So only option $$A$$ is possible.
Steps of construction
Step 1. Draw a line segment $$AB=6\ \ cm$$
Step 2. Assuming $$A$$ a centre draw an arc of radius $$8 \ \ cm$$
Step 3. Now assuming $$B$$ as centre draw an arc of $$7 \ \ cm$$ 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 2
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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 step is not a part of construction?
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 $$C$$.

A
1

B
2

C
3

D
none of these

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, (D) will be correct.
Question 3
1 / -0

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the second step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass.
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle.
5. Draw the base side $$ QR = 8\ cm $$.

A
$$2$$

B
$$1$$

C
$$4$$

D
$$5$$

E
$$3$$

Solution

Step 1. Draw a line $$QR=8\ \ cm$$
Step 2. At point $$Q$$ ,draw an angle of $$90^{\circ}$$
Step 3. From $$R$$ cut an arc $$PR=10\ \ cm$$ using compass.
Step 4. Name the point of intersection of the arm of angle $$90^{\circ}$$ and the arc in step $$3$$ , as $$P$$
Step 5. Join $$P$$ to $$Q$$. $$PQR$$ is required triangle.
So the second step is $$1$$
Option $$B$$ is correct.
Question 4
1 / -0

For construction of a $$\triangle PQR$$, when $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the fifth step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass.
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle.
5. Draw the base side $$ QR = 8\ cm $$.

A
$$2$$

B
$$3$$

C
$$1$$

D
$$5$$

E
$$4$$

Solution

Step 1. Draw a line $$QR=8\ \ cm$$
Step 2. At point $$Q$$ ,draw an angle of $$90^{\circ}$$
Step 3. From $$R$$ cut an arc $$PR=10\ \ cm$$ using compass.
Step 4. Name the point of intersection of the arm of angle $$90^{\circ}$$ and the arc in step $$3$$ , as $$P$$
Step 5. Join $$P$$ to $$Q$$. $$PQR$$ is required triangle.
So the fifth step is $$4$$
Option $$E$$ is correct.
Question 5
1 / -0

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the first step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass .
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle.
5. Draw the base side $$ QR = 8\ cm $$.

A
$$2$$

B
$$1$$

C
$$3$$

D
$$5$$

E
$$4$$

Solution

Step 1. Draw a line $$QR=8\ \ cm$$
Step 2. At point $$Q$$ ,draw an angle of $$90^{\circ}$$
Step 3. From $$R$$ cut an arc $$PR=10\ \ cm$$ using compass.
Step 4. Name the point of intersection of the arm of angle $$90^{\circ}$$ and the arc in step $$3$$ , as $$P$$
Step 5. Join $$P$$ to $$Q$$. $$PQR$$ is required triangle.
So the first step is $$5$$
Option $$D$$ is correct.
Question 6
1 / -0

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the fourth step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass .
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle.
5. Draw the base side $$ QR = 8\ cm $$.

A
$$5$$

B
$$1$$

C
$$2$$

D
$$3$$

E
$$4$$

Solution

Step 1. Draw a line $$QR=8\ \ cm$$
Step 2. At point $$Q$$ ,draw an angle of $$90^{\circ}$$
Step 3. From $$R$$ cut an arc $$PR=10\ \ cm$$ using compass.
Step 4. Name the point of intersection of the arm of angle $$90^{\circ}$$ and the arc in step $$3$$ , as $$P$$
Step 5. Join $$P$$ to $$Q$$. $$PQR$$ is required triangle.
So the fourth step is $$3$$
Option $$D$$ is correct.
Question 7
1 / -0

For construction of a $$\triangle PQR$$, where $$\displaystyle QR=8\ cm, PR=10\ cm$$ and $$\angle Q=90^{\circ}$$, its steps for construction is given below in jumbled form. Identify the third step from the following.

1. At point $$ Q $$, draw an angle of $$ {90}^{\circ} $$.
2. From $$ R $$ cut an arc of length $$ PR = 10.0 \ cm $$ using a compass.
3. Name the point of intersection of the arm of the angle $$ {90}^{\circ} $$ and the arc drawn in step 3, as $$ P $$.
4. Join $$P $$ to $$ Q $$ . $$ PQR $$ is the required triangle.
5. Draw the base side $$ QR = 8\ cm $$.

A
$$3$$

B
$$4$$

C
$$2$$

D
$$5$$

E
$$1$$

Solution

Step 1. Draw a line $$QR=8\ \ cm$$
Step 2. At point $$Q$$ ,draw an angle of $$90^{\circ}$$
Step 3. From $$R$$ cut an arc $$PR=10\ \ cm$$ using compass.
Step 4. Name the point of intersection of the arm of angle $$90^{\circ}$$ and the arc in step $$3$$ , as $$P$$
Step 5. Join $$p$$ to $$Q$$. $$PQR$$ is required triangle.
So the third step is $$2$$
Option $$C$$ is correct.
Question 8
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 first 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, (D) will be correct.
Question 9
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 includes the following steps, then answer the following question:
Which of the following is the 3rd 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 $$3:$$ Draw a line segment $$AB= 5 \ cm.$$
Step $$4:$$ Now assuming $$B$$ as centre draw an arc of $$4 \ cm.$$ intersecting the previous arc at $$C.$$

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, option $$D$$ will be correct.
Question 10
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Construct a right angle triangle ABC such as $$AC=5 cm ,BC=3 cm$$ , $$\angle B=90^o$$
What would be the length of $$AB$$ after construction?

A
$$2$$ cm

B
$$4$$ cm

C
$$5$$ cm

D
$$3$$ cm

Solution

In triangle in $$\triangle \ ABC$$, by Pythagoras theorem

$$AC^2=AB^2+AC^2$$

Given, $$AB=5 \ cm, \ BC=x$$

$$5^2=x^2+3^2$$

$$x^2=5^2-3^2=25-9=16$$

$$x=\sqrt{16}=4 \ cm$$
Hence, $$AB=4$$ cm.

Or
Simply after constructing, we can measure AB side.