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Maths 3 Mark Question

Geometrical Constructions · Maharashtra Board STD 6 (MSBSHSE - Semi English Medium). 7 questions.

Questions

3 Mark Question

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7 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
Draw ray PQ as shown in the figure. Using the protractor, make an angle of 15° with one hand PQ.
Answer
Draw a ray PQ as given in the question.
Place the protractor on the ray PQ such that its center coincides with the point P and the diameter of the protractor coincides with PQ.
Mark a point B against the mark of 15° on the protractor.
Remove the protractor and draw PB. $\angle\text{QPB}$ is the required angle of 15°.
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Question 23 Marks
Construct line segments whose lengths are:
4.8cm.
Answer
Draw a line L on the paper and mark a point A on it.
Take a compass and place its metal point at zero mark of the ruler.
Adjust the compass such that the pencil point is at 4.8cm mark on the ruler.
Now, take the compass to L such that its metal point is on point A.
Mark a small mark at B on L corresponding to the pencil point of the compass.
AB is the required line segment of 4.8cm.
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Question 33 Marks
Construct line segments whose lengths are:
12cm 5mm
Answer
Draw a line L on the paper and mark a point A on it.
Take a compass and place its metal point at zero mark of the ruler.
Adjust the compass such that the pencil point gets placed at the point which is 5 small points from the mark of 12cm to 13cm of the ruler.
Now, take the compass to L such that its metal point is on A.
Mark a small mark at B on L corresponding to the pencil point of the compass.
AB is the required line segment of 12cm 5mm.
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Question 43 Marks
Construct line segments whose lengths are:
7.6cm
Answer
Draw a line L on the paper and mark a point A on it.
Take a compass and place its metal point at zero mark of the ruler.
Adjust the compass such that the pencil point gets placed at the point which is 6 small points from the mark of 7cm to 8cm of the ruler.
Take the compass to L such that its metal point is on A.
Mark a small mark at B on the line L corresponding to the pencil point of the compass.
AB is the required segment of 7.6cm.
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Question 53 Marks
Draw a line PQ. Take a point R on it. Draw a line perpendicular to PQ and passing through R.
Ruler and compasses.
Answer
Draw a line PQ and take a point R on it.
With R as centre and taking a convenient radius, construct an arc touching the line PQ at two points A and B. Now, with A and B as centres and radius greater than AR, construct two arcs cutting each other at S.
Join RS and extend it in both directions.
This is the required line, which is perpendicular to PQ and passes through R.
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Question 63 Marks
Draw ray RS as shown in the figure. Using the protractor, make an angle of 138° with one hand PQ.
Answer
Draw a ray RS as given in the question.
Place the protractor on ray RS such that its centre coincides with the point R and diameter of the protractor coincides with RS.
Mark a point T against the mark of 138° on the protractor.
Remove the protractor and draw RJ.
$\angle\text{SRT}$ the required angle of 138°.
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Question 73 Marks
Draw a line PQ. Take a point R on it. Draw a line perpendicular to PQ and passing through R.
Using ruler and a set-square.
Answer
Draw a line PQ and take a point R on it.
Place a set-square, such that its one arm of the right angle is along the line PQ .
Without disturbing the position of the set-square, place a ruler along its edge.
Now, without disturbing the position of the ruler, remove the set-square and draw a line MN through point R.
MN is the required line perpendicular to line PQ passing through R.
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