Practical Geometry Test

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Practical Geometry Test - 5

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Question 1
1 / -0

Construct a triangle $$ABC$$ in which $$AB = 5 cm$$ and $$BC = 4.6 cm$$ and $$AC = 3.7 cm$$
Steps for the construction is given in jumbled form.Choose the appropriate sequence for the above
1) With radius as $$5\ cm$$ from $$C$$, cut an arc.
2)These arcs will intersect at point $$A$$. Join $$AB$$ and $$AC$$. $$ABC$$ is the required triangle.
3)Draw a line segment $$BC = 4\ cm.$$
4)With radius as $$3$$ cm from $$B$$, cut the arc.

A
$$1,4,3,2$$

B
$$4,3,2,1$$

C
$$3,1,4,2$$

D
$$4,1,3,2$$

Solution

Correct sequence is:
1. Draw a line segment $$AB=4$$ cm.
2. With radius $$5$$ cm from $$C$$ , cut an arc.
3. With radius $$3$$ cm from $$B$$ , cut an arc.
4. The arc will intersect at point $$A$$, Join $$AB$$ and $$AC$$ .$$ABC$$ is required triangle.
So correct sequence is $$3,1,4,2$$
So option $$C$$ is correct.
Question 2
1 / -0

Which of the following steps is INCORRECT while constructing $$\triangle XYZ$$ if it is given that $$XY = 6 cm, \angle ZXY = 30^o$$ and $$\angle XYZ = 100^o$$
Step 1: Draw line $$XY$$ of length $$6 cm$$.
Step 2: At $$X$$, draw a ray $$XP$$ making an angle of $$30^o$$ with $$XY$$.
Step 3: At $$Y$$, draw a ray $$YQ$$ making an angle of $$100^o$$ with $$YX$$.
Step 4: The point of intersection of the two rays $$XY$$ and $$YQ$$ is $$Z$$.

A
Step 1

B
Step 2 and Step 4

C
Step 3

D
Step 4

Solution

Given $$\triangle XYZ$$ and $$XY=6$$ $$cm,\angle ZXY=30^o, \angle XYZ=100^o$$
So, steps of drawing $$\triangle XYZ$$
Step $$I:$$ Draw a line $$XY$$ of length $$6$$ $$cm$$ as shown in IMAGE $$01$$.
Step $$II:$$ Draw a ray $$XP$$ from $$X$$ making angle of $$30^o$$ with $$XY$$ line as shown in IMAGE $$02$$.
Step $$III:$$ Draw a ray $$YQ$$ from point $$Y$$ making an angle of $$100^o$$ with $$XY$$ as shown in IMAGE $$03$$.
Step $$IV:$$ Extend $$XP$$ and $$YQ$$ ray and where they will meet will be the point $$Z$$ of $$\triangle XYZ$$.
So, point of intersection will be $$Z$$ from $$XP$$ and $$YQ$$ not $$XY$$ and $$YQ$$ not $$XY$$ and $$YQ$$.
Question 3
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Which of the following steps is INCORRECT, while constructing $$\triangle$$LMN, right-angled at M, given that LN = 5 cm and MN = 3 cm?
Step 1. Draw MN of length 3 cm.
Step 2. At M, draw MX $$\perp$$ MN. (L should be somewhere on this perpendicular).
Step 3. With N as the center, draw an arc of radius 5 cm. (L must be on this arc since it is at a distance of 5 cm from N).
Step 4. L has to be on the perpendicular line MX as well as on the arc drawn with center N. Therefore, L is the meeting point of these two and $$\triangle$$LMN is obtained.

A
Only Step 4

B
Both Step 2 and Step 3

C
Only Step 2

D
None of these

Solution
Question 4
1 / -0

Construct a triangle $$ABC$$, in which $$AB = 5.5 \ cm, AC = 6.5 \ cm$$ and $$\angle BAC = 75^{\circ}$$.
Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) At $$A$$, construct a line segment $$AE$$, sufficiently large, such that $$\angle BAE=75^\circ$$, use protractor to measure $$75^\circ$$.
2) Draw a line segment which is sufficiently long using ruler.
3) With $$A$$ as centre and radius $$6.5\ cm$$, draw an arc cutting $$AE$$ at C. Join $$BC$$. Hence, $$ABC$$ is the required triangle.
4) Locate points $$A$$ and $$B$$ on it such that $$AB = 5.5\ cm$$.

A
$$2,4,1,3$$

B
$$2,1,4,3$$

C
$$1,2,4,3$$

D
$$4,2,1,3$$

Solution

The following is the correct order of steps for constructing $$\Delta ABC$$
i) Draw a line segment which is sufficiently long using ruler.
ii) Locate points $$A$$ and $$B$$ on it such that $$AB=5.5 \ cm$$.
iii) At $$A$$ construct a line segment $$AE$$ , sufficiently large, such that $$\angle BAE=75^\circ$$, use protractor to measure $$75^\circ$$.
iv) With $$A$$ as centre and radius $$6.5 \ cm$$ draw an arc cutting $$AE$$ at $$C$$. Join $$BC$$. Hence, $$ABC$$ is the required triangle.

So, the correct sequence of given steps is $$2,4,1,3$$.
Question 5
1 / -0

The steps to construct a line parallel to a given line is given below (in random order):

Step 1 : Place the pointed tip of the compasses at C and adjust the opening so that the pencil tip is at D
Step 2 : Take any point B on l and join B to A
Step 3 : Take a line ‘l’ and a point ‘A’ outside ‘l’
Step 4 : Now with A as centre and the same radius as in the previous step, draw an arc EF cutting AB
at G
Step 5: With B as centre and a convenient radius, draw an arc cutting l at C and BA at D
Step 6 : With the same opening as in the previous step and with G as centre, draw an arc cutting the
arc EF at H. Now, join AH to draw a line ‘m'

The second step is

A
Step 1

B
Step 2

C
Step 3

D
Step 4

Solution

From the above given steps, it is clear that $$Step 2 =$$ $$\textbf{Take any point B on I and join B to A} $$ is the second step. Hence Option $$B$$
Question 6
1 / -0

The steps to construct a line parallel to a given line is given below (in random order):

Step 1 : Place the pointed tip of the compasses at C and adjust the opening so that the pencil tip is at D
Step 2 : Take any point B on l and join B to A
Step 3 : Take a line l and a point A outside l
Step 4 : Now with A as centre and the same radius as in the previous step, draw an arc EF cutting AB
at G
Step 5: With B as centre and a convenient radius, draw an arc cutting l at C and BA at D
Step 6 : With the same opening as in the previous step and with G as centre, draw an arc cutting the
arc EF at H. Now, join AH to draw a line m'

The first step is

A
Step 1

B
Step 2

C
Step 3

D
Step 4

Solution

To construct a line parallel to a given line, the first step is to take a line and a point outside the line. Hence from the given steps, we can see that the above corresponds to step 3. $$\Rightarrow$$ Option $$C$$
Question 7
1 / -0

Let l be a line and P be a point not on l. Through P, draw a line m parallel to l. Now join P to any point Q on l.
Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet l at S. What shape do the two sets of parallel lines enclose?

A
Triangle

B
One pair of parallel lines

C
Parallelogram

D
Only one line

Solution
Question 8
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Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

The steps are as follows (in random order):
Step (a) Take PX = 4 cm on line n.
Step (b) At point X, again draw a perpendicular line m.
Step (c) Draw a line l and take a point P on it.
Step (d) At point P, draw a perpendicular line n.
The first step is

A
Step (a)

B
Step (b)

C
Step (c)

D
Step (d)

Solution
Question 9
1 / -0

The steps to construct a line parallel to a given line is given below (in random order):

Step 1 : Place the pointed tip of the compasses at C and adjust the opening so that the pencil tip is at D
Step 2 : Take any point B on l and join B to A
Step 3 : Take a line ‘l’ and a point ‘A’ outside ‘l’
Step 4 : Now with A as centre and the same radius as in the previous step, draw an arc EF cutting AB
at G
Step 5: With B as centre and a convenient radius, draw an arc cutting l at C and BA at D
Step 6 : With the same opening as in the previous step and with G as centre, draw an arc cutting the
arc EF at H. Now, join AH to draw a line ‘m'

The third step is

A
Step 2

B
Step 3

C
Step 4

D
Step 5

Solution
Question 10
1 / -0

The steps to construct a line parallel to a given line is given below (in random order):

Step 1 : Place the pointed tip of the compasses at C and adjust the opening so that the pencil tip is at D
Step 2 : Take any point B on l and join B to A
Step 3 : Take a line ‘l’ and a point ‘A’ outside ‘l’
Step 4 : Now with A as centre and the same radius as in the previous step, draw an arc EF cutting AB
at G
Step 5: With B as centre and a convenient radius, draw an arc cutting l at C and BA at D
Step 6 : With the same opening as in the previous step and with G as centre, draw an arc cutting the
arc EF at H. Now, join AH to draw a line ‘m'

The fifth step is

A
Step 1

B
Step 2

C
Step 3

D
Step 4