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LINE SEGMENT OPERATIONS
In geometry, a line segment is a part of a line that is bounded by two distinct endpoints, and contains every point on the line
between its endpoints. Line segments are generally labeled with two capital letters corresponding to their endpoints.
1. LINE SEGMENT COPYING
Start with a line segment AB that we will copy.
STEPS:
1.Draw a ray from point A´.
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2.With the compass take the length AB.
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3.With the length AB kept with the compass set the center on the ray´s point A´ and draw an arc obtaining B´.
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3.With the length AB kept with the compass set the center on the ray´s point A´ and draw an arc obtaining B´.
2. LINE SEGMENTS ADDITION
Given the line segments AB and CD, we have to add them up.
STEPS:
1.Draw a ray from the point A´.
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2.With the compass take the length AB and copy it on the ray from A´, obtaining B´.
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2.With the compass take the length AB and copy it on the ray from A´, obtaining B´.
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2.With the compass take the length AB and copy it on the ray from A´, obtaining B´.
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3.We take the length CD and copy it on the ray from B´obtaining the segment C´D´.
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3.We take the length CD and copy it on the ray from B´obtaining the segment C´D´.
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3.We take the length CD and copy it on the ray from B´obtaining the segment C´D´.
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3.We take the length CD and copy it on the ray from B´obtaining the segment C´D´.
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4.The solution is the segment A´D´.
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3. LINE SEGMENTS SUBTRACTION
Given the line segments AB and CD, we have to construct a segment whose length is the difference of both of them.
STEPS:
1.Draw a ray from the point A´.
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1.Take with the compass the AB length, the longest one, and copy it on the ray from A´, obtaining B´ (AB line segment copying).
STEPS:
1.Take with the compass the AB length, the longest one, and copy it on the ray from A´, obtaining B´ (AB line segment copying).
STEPS:
1.Take with the compass the AB length, the longest one, and copy it on the ray from A´, obtaining B´ (AB line segment copying).
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2.Take with the compass the length CD, the smallest one, and copy it on the ray from A´, obtaining C´D´.
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2.Take with the compass the length CD, the smallest one, and copy it on the ray from A´, obtaining C´D´.
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2.Take with the compass the length CD, the smallest one, and copy it on the ray from A´, obtaining C´D´.
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1.The differences of length, length from D´to B´, is the result.
4. LINE SEGMENT MULTIPLICATION
Given a segment AB we have to construct a segment 3 times longer than AB.
STEPS:
1. Draw a ray from the point A´.
STEPS:
1. With the compass take the length AB and copy it on the ray from A´.
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1. With the compass take the length AB and copy it on the ray from A´.
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2.Repeat the operation three times.
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2.Repeat the operation three times.
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3.The result is the segment A´B´ which is three times as long as AB.
5. DIVIDING A SEGMENT INTO SEVERAL EQUAL PARTS
Draw the given segment AB. This is the segment that we want to divide.We are going to divide it into 3 parts.
STEPS:
1.From point A draw an oblique ray (r). It doesn´t matter the angle you take.
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2.Choose a measure with your compass and from point A draw arcs on the oblique ray. You have to draw as many arcs as parts you need.
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2.Choose a measure with your compass and from point A draw arcs on the oblique ray. You have to draw as many arcs as parts you need.
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2.Choose a measure with your compass and from point A draw arcs on the oblique ray. You have to draw as many arcs as parts you need.
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3.Join the last point of the oblique ray, 3, with point B.
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4.Draw parallels using your set square to the segment 3B from the other points on the ray.
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4.Draw parallels using your set square to the segment 3B from the other points on the ray.
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4.Draw parallels using your set square to the segment 3B from the other points on the ray.
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5.The result is the segment AB divided into three parts. Here we have divided the segment into three parts, but you can divide the segment into as many parts as you need.
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5.The result is the segment AB divided into three parts. Here we have divided the segment into three parts, but you can divide the segment into as many parts as you need.
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