Line Segments
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PRACTICAL GEOMETRY Duplicating Line Segments 1. Using ruler and compasses, construct a line segment whose length is equal to that of a given line segment AB. Steps of construction 1. Given AB whose length is not known.
2. Draw a line l
3. Fix the metal tip of the compasses at A and pencil at B.
4. Take any point C on line l and place metal tip of the compasses on C.
5. Without disturbing the opening of the compasses draw an arc, which cuts l at D.
Now, CD is the required line segment. 2. Using a ruler, draw to line segments AB = 5 cm and CD = 3 cm. Without using a ruler, construct a line segment whose length is equal to a. AB - CD
b. AB + CD Steps of construction a. AB - CD 1. Draw line segments AB and CD of lengths 5 cm and 3 cm respectively
2. Now fix the metal tip of the compasses at C and open it such that the pencil tip is exactly at D. 3. Without disturbing the opening of the compasses, fix the metal tip at A and draw arc E which cuts AB at E. EB is the required length of AB – CD Steps of construction a. AB + CD 1. Using a ruler, draw a line l
2. Mark a point P on it. 3. Keep the metal tip of the compasses at A of line AB and open it to point B. 4. Without disturbing opening of the compasses, place the metal tip of the compasses at P and draw arc Q. Now PQ = AB. 5. Now fix the metal tip of the compasses at C of line segment CD and open the compasses so that the pencil tip reaches D. 6. Without disturbing the opening of the compasses, place the metal tip at Q and draw arc R. Now QR = CD. Hence, PR = AB + CD PR is the required length 3. A line segment PQ is given. Using ruler and compasses, construct XY such that XY = 3PQ Steps of construction 1. Draw line l and mark a point A on it.
2. Fix the metal tip of the compasses at P and pencil tip at Q.
3. Without disturbing the opening of the compasses, place the metal tip at A and draw an arc which cuts l at B. 4. With the same opening place the metal tip at B and draw an arc which cuts l at C. 5. Again with the same opening, place the metal tip of the compasses at C, draw an arc which cuts l at D. AD is the required segment.
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2. Draw a line l
3. Fix the metal tip of the compasses at A and pencil at B.
4. Take any point C on line l and place metal tip of the compasses on C.
5. Without disturbing the opening of the compasses draw an arc, which cuts l at D.
Now, CD is the required line segment. 2. Using a ruler, draw to line segments AB = 5 cm and CD = 3 cm. Without using a ruler, construct a line segment whose length is equal to a. AB - CD
b. AB + CD Steps of construction a. AB - CD 1. Draw line segments AB and CD of lengths 5 cm and 3 cm respectively
2. Now fix the metal tip of the compasses at C and open it such that the pencil tip is exactly at D. 3. Without disturbing the opening of the compasses, fix the metal tip at A and draw arc E which cuts AB at E. EB is the required length of AB – CD Steps of construction a. AB + CD 1. Using a ruler, draw a line l
2. Mark a point P on it. 3. Keep the metal tip of the compasses at A of line AB and open it to point B. 4. Without disturbing opening of the compasses, place the metal tip of the compasses at P and draw arc Q. Now PQ = AB. 5. Now fix the metal tip of the compasses at C of line segment CD and open the compasses so that the pencil tip reaches D. 6. Without disturbing the opening of the compasses, place the metal tip at Q and draw arc R. Now QR = CD. Hence, PR = AB + CD PR is the required length 3. A line segment PQ is given. Using ruler and compasses, construct XY such that XY = 3PQ Steps of construction 1. Draw line l and mark a point A on it.
2. Fix the metal tip of the compasses at P and pencil tip at Q.
3. Without disturbing the opening of the compasses, place the metal tip at A and draw an arc which cuts l at B. 4. With the same opening place the metal tip at B and draw an arc which cuts l at C. 5. Again with the same opening, place the metal tip of the compasses at C, draw an arc which cuts l at D. AD is the required segment.
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