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Question 13 Marks
Mark two points, A and B on a piece of paper and join them. Measure this length. Draw a line segment CD that is:
Half AB.
Answer
Mark two points, A and B on a piece of paper and join them as follows:
To measure the length of AB, place the ruler with its edge along AB, such that the zero mark of the cm side of the ruler coincides with point A, as shown in the figure. Now, read the mark on the ruler, which corresponds to the point B. The reading on the ruler at point B is the length of the line segment AB. Here, AB = 5.6cm To draw the line segment that is half AB, we draw a line/ and take a point C on it. Now, using a ruler, we measure the line segment AB and here, AB = 5.6cm Half of AB = 5.62 = 2.8cm Now, we take a divider and open it so much that its end of one hand is at 0 and end of the another hand is at 2.8cm. Then, we lift the divider and place one end at C and the other end on the line l at point D.
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Question 23 Marks
Mark two points, A and B on a piece of paper and join them. Measure this length. Draw a line segment CD that is:
Twice AB.
Answer
Mark two points, A and B on a piece of paper and join them as follows:
To measure the length of AB, place the ruler with its edge along AB, such that the zero mark of the cm side of the ruler coincides with point A, as shown in the figure. Now, read the mark on the ruler, which corresponds to the point B. The reading on the ruler at point B is the length of the line segment AB. Here, AB = 5.6cm To draw the line segment twice AB, draw a line/ and take a point C on it. Now, take a divider and open it such that the end points of both its arms are at A and B. Then, lift the divider and without disturbing its opening, place one end-point at C and the other end-point on the line 1, as shown in the figure. Lift the divider and place one end-point at E and the other end-point on the line 1, opposite C. Name this point D.
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Question 33 Marks
Construct the following angles using set-squares:
105°
Answer
105° Place 30° set-square and make an angle 60° by drawing the rays BA and BC as shown in figure.
Now place the vertex of 45° of the set –square on the ray BA as shown in figure and draw the ray BD. The angle so formed is 105° Therefore, $\angle\text{DBC}=150^{\circ}$
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Question 43 Marks
Construct the following angles using set-squares:
105°
Answer
Place the vertex of 45° of the set-square and make angle of 90° by drawing the rays BD and BC as shown in the figure
Now, place the vertex of 30° of the set-square on the ray BS as shown in the figure and draw the ray BA The angle so formed is 150°. Therefore, $\angle\text{ABC}=150^{\circ}$
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Question 53 Marks
If AB = 7.5cm and CD = 2.5cm, construct a segment whose length is equal to:
AB - CD
Answer
Given: AB= 7.5cm and CD = 2.5cm Draw AB and CD
Draw a line l and take a point E on it. Now, take a divider and open it such that ends of both the arms are at A and B. Then, we lift the divider and place its one end at E and other end (F) and on the line l as shown in figure. Now, reset the divider in such a way that the end of its one hand is at C and the end of the other hand is at D. Then, we lift the divider and place its one end at E and other end (G) on the line l as shown in the figure. FG is required line segment, whose length is equal to (AB - CD)
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Question 63 Marks
If AB = 7.5cm and CD = 2.5cm, construct a segment whose length is equal to:
2AB
Answer
Given: AB= 7.5cm and CD = 2.5cm Draw AB and CD
Draw a line l and take a point E on it. Now a take a divider and open it such that the ends of both its arms are at A and B. Then, we lift the divider and place its one end at E and other end (say F) on the line l as shown in the figure. Again, lift the divider and place its one end F and other end on the line l, opposite to E. Let this point be G. EG is required line segment, whose length is equal to 2AB.
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Question 73 Marks
Mark two points, A and B on a piece of paper and join them. Measure this length. Draw a line segment CD that is:
Collinear with AB and is equal to it.
Answer
Mark two points, A and B on a piece of paper and join them as follows:
To measure the length of AB, place the ruler with its edge along AB, such that the zero mark of the cm side of the ruler coincides with point A, as shown in the figure. Now, read the mark on the ruler, which corresponds to the point B. The reading on the ruler at point B is the length of the line segment AB. Here, AB = 5.6cm
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Question 83 Marks
The end-point P of a line-segment PQ is against 4cm mark and the end-point Q is against the mark indicating 14.8cm on a ruler. What is the length of the segment PQ?
Answer

Extend the line segment QP towards point zero of the ruler and take a point 0 on the extended line QP corresponding to point zero on the ruler.
From the figure, we can say:
OP = 4cm and OQ = 14.8cm
Now, PQ = OQ - OP
= (14.8 - 4)cm
= 10.8cm
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Question 93 Marks
Given a line BC and a point A on it, construct a ray AD using set squares so that $\angle\text{DAC}$ is:
150°
Answer
Draw a line BC and take a point A on it. Place 30° set-square on the line BC such that its vertex of 30° angle lies on point A and one edge coincides with the ray AB as shown in the figure. Draw the ray AD.
Therefore, $\angle\text{DAB}=30^{\circ}$ We know that angle on one side of the straight line will always add to 180° Therefore, $\angle\text{DAB}+\angle{\text{DAC}}=180^{\circ}$ Therefore, $\angle\text{DAC}=150^{\circ}$
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Question 103 Marks
What is the difference between line, a line segment and a ray?
Answer

A line can be drawn to infinity in both the directions. AB is a line.
A line segment has both ends fixed. EF is a line segment. A ray has one end fixed and another end can be drawn to infinity. CD is a ray.
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Question 113 Marks
Mark two points, A and B on a piece of paper and join them. Measure this length. Draw a line segment CD that is:
Three times AB.
Answer
Mark two points, A and B on a piece of paper and join them as follows:
To measure the length of AB, place the ruler with its edge along AB, such that the zero mark of the cm side of the ruler coincides with point A, as shown in the figure. Now, read the mark on the ruler, which corresponds to the point B. The reading on the ruler at point B is the length of the line segment AB. Here, AB = 5.6cm To draw the line segment three times A, we draw a line / and take a point C on it. Now take a divider and open it, such that the end-points of both its arms are at A and B. Then, we lift the divider and place one end-point at C and the other end-point on the line 1, as shown in the figure. Let this point be E. Again, lift the divider and place one end-pint at E and the other end-point on the line 1, opposite to C. Let this point be F. Again, lift the divider and place one end-point at F and the other end-point on the line 1, opposite to C. Name this point D.
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Question 123 Marks
If AB = 7.5cm and CD = 2.5cm, construct a segment whose length is equal to:
AB + CD
Answer
Given: AB= 7.5cm and CD = 2.5cm Draw AB and CD
We draw a line l and take a point E on it. Now, take a divider and open it such that the ends of both its arms are A and B. The, we lift the divider end (F) on the line l, as shown in the figure. Now, reset the divider in such a way that the end of its one hand is at C and the end of the other hand is at D. Then, we lift the divider and place its one end at F and another end (G) on the line l opposite to E as shown in the figure. EG is required line segment, whose length is equal to (AB + CD)
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Question 133 Marks
Construct the following angles using set-squares:
75°
Answer
Place 45° set-square and make an angle of 45° by drawing the rays BD and BC as shown in the figure.
Now place the vertex of 30° of the set- square on the ray BD as shown in the figure and draw the ray BA. The angle so formed is 75°. Therefore, $\angle\text{ABC}=75^{\circ}$
(Line BD is hidden)
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Question 143 Marks
If AB = 7.5cm and CD = 2.5cm, construct a segment whose length is equal to:
3CD
Answer
Given: AB= 7.5cm and CD = 2.5cm Draw AB and CD
Draw a line l and take a point E on it. Now take a divider and open it such that the ends of both its arms are at C and D. Then, we lift the divider and place its end at E on it and other end (F) on the line l, as shown in the figure. Again, we lift the divider end (G) on the l opposite to C. Again, lift the divider end (G) on the line l opposite to C. Again, lift the divider and place its one end at G and another end (H) on the line l, opposite to E. EH is required line segment, whose length is equal to 3CD.
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