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Constructing of Copy of Line Segments, in mathematics, is similar to a drawing that produces a visual outcome. Every shape begins with a point and then extends to be a line, a line segment or a curve. Drawings are just rough sketches that help to give us an idea, whereas constructions are step-by-step processes used to create accurate geometric figures. By definition, a line segment is a part of a line which connects two points within a line.
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Key Takeaways - Constructing of Copy of Line Segments, Line segment, Copy of line segments, Lines, Intersecting lines, Perpendicular lines, Parallel lines
Also read: Isosceles Triangle Theorems
Geometric Construction
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Geometric construction is a process of constructing geometric figures using geometric tools such as a pencil, ruler, compass. There are no measurements, no numbers as this is the purest form of geometry.
A ruler is used to draw the line segments and measure their lengths whereas a compass is used to construct arcs and circles and mark off equal length.
Lets learn geometric construction of line step by step below
Geometric line
X point is a small dot which is the starting point of a line segment. By definition, a line segment is a part of a line which connects two points within a line. Various numbers of the line segments provide us with different figures. A line segment is denoted by its two endpoints. In the figure, p is a line and XY is the line segment on the line p.
Also read- Arcs
Procedure for Constructing of Copy of Line Segments
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A ruler and compass pair can be used to create a line segment of a specific length. Using one of the above approaches, we can quickly create a copy of a given line segment. When we only use a ruler the construction of line segments is not as precise. As a result, using a ruler and compass to make a copy of line segments is always preferable. To begin the copying method, you must first draw a straight line for the provided measurement. See the steps below-
Step 1: You are given line segment AB to copy.
Step 2: Draw a line segment which is longer in length than the AB line segment and mark one of its endpoints as C.
Step 3: Open the compass in order to keep the anchor on one endpoint of the AB line segment and the pencil point is on the other endpoint.
Step 4: Keeping the opening of the compass in the same position, place the anchor on the point C on the second line segment. Make a mark that crosses this line segment. Mark the point where the pencil crosses the line segment and label it as D.
Line segment CD should be similar in length in comparison to the line segment AB. Line segments CD and AB are congruent.
Types of Line Segment
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A segment is a component of something, such as a section of a line with identifiable beginning and ending points.
There are three types of line segments
- Intersecting lines
- Parallel lines
- Perpendicular lines
Intersecting lines
Intersecting lines are formed when two or more lines cross each other. The point of intersection is when the lines crossing each other have a common point that is present on all intersecting lines. An example of an intersecting line is scissors. A pair of scissors has two arms and both of them form intersecting lines.
Parallel lines
Lines that do not overlap or connect at any point in a plane are called parallel lines. They are parallel and distant from each other at all times. Non-intersecting lines are known as parallel lines. Parallel lines can also be said to meet at infinity.
Perpendicular lines
Perpendicular lines are intersecting lines that make a 90-degree angle (right angle). If two lines are intersecting each other at a right angle, then the lines are perpendicular to each other. When a line is perpendicular to the plane, it is said to be perpendicular to all of the plane's points or to each of the plane's lines that it intersects.
Things to Remember
- A line segment is a part of a line that connects two points within a line.
- A combination of ruler and compass is a better approach to construct a copy of the line segment.
- A line segment is bounded by two end-point
- Perpendicular lines always intersect at 90 degrees but not all intersecting lines are perpendicular.
Also read: First Order Differential Equation
Sample Questions
Ques- Draw a line segment of length 4.5cm using ruler and compass. (4 marks)
Ans- (1) Draw a line l. Mark a point A on a line l.
(2) Place the compass pointer on the ruler at 0 mark. Open the compass and place the pencil point up to the 4.5 cm mark.
(3) One must be careful while opening the compasses so that it doesn't change, place the pointer on A and swing an arc to cut l at B.
(4) is a line segment of required length.
Ques - Draw a line segment of length 7.8 cm using ruler and compasses. (4 marks)
Ans - (1) Draw a line l. Mark a point A on a line l.
(2) Place the compass pointer on the ruler at the 0 mark and place the pencil point up to the 7.8 cm mark.
(3) Place the compass carefully so that the measurement does not change and place the pointer on A and swing an arc to cut l at B.
(4) AB is a line segment of required length.
Ques- Construct AB of length 6.2 cm. From this cut off of length AC 2.8 cm. Measure BC. (5 marks)
Ans- (1) Draw a line l. Mark a point A on a line l.
(2) Place the compass pointer on the zero mark of the ruler. Place the pencil and mark B at 6.2cm.
(3) Again place the compass pointer on the zero mark of the ruler and place the pencil point at the 2.8cm, marking the point as C.
(4) Cautiously open the compasses in order to not change the measurement, place the pointer on A and swing an arc to cut l at C.
(5) AC is a line segment of required length.
(6) Measure of BC = 6.2-2.8 = 3.4 cm.
Ques- Given AB of length 5.2 cm, construct PQ such that the length of PQ is twice that of AB. Verify the measurement. (5 marks)
Ans- (1) Draw a line l. Mark a point A on a line l.
(2) Place the compass pointer on the ruler at the zero mark. Open it to place the pencil point up to the 5.2cm mark say this B.
(3) We know that 10.4 is twice of the given line segment.
(4) Draw another line l. Mark a point P on a line l.
(5) Now place the compass pointer on the zero mark of the ruler. Open it to place the pencil point up to the 5.2cm mark say this X.
(6) Without changing the compass setting and from point X draw another arc say this point be Q.
(7) PQ is the required line segment of length 10.4 cm.
Ques- Given two line segments AB and CD of length 4.2cm and 4.8cm respectively. Construct a line segment EF equal to the sum of the measures of AB and CD. (4 marks)
Ans- (1) Draw a ray EH longer than the combined lengths of AB and CD .
(2) Using compasses, measure 4.2cm and cut off EG= AB on the ray EH .
(3) Again, using the compasses, measure 4.8 and mark off GF = CD along GH.
(4) The length of EF is equal to the sum of the lengths of AB and CD
Ques- Draw any line segment AB. Without measuring AB, construct a copy of AB. (4 marks)
Ans- (1) Given AB whose length is not known.
(2) Fix the compass pointer on A and the pencil end on B. The opening of the instrument now gives the length of AB .
(3) Draw any line l. Choose a point C on l. Without changing the compass setting, place the pointer on C.
(4) Swing an arc that cuts l at a point, say D. Now the CD is a copy of AB.
Ques- Given two line segments AB and CD whose length is not known. Draw a line XY equal to the sum of AB and CD. (5 marks)
Ans- (1) Given two line segments AB and CD whose length is not known.
(2) Draw a line l.
(3) Using a compass to measure the length of AB . Now taking the compasses pointer on X and without changing compasses setting, draw an arc on the line, say this point as P.
(4) Measure the length of the CD . Now taking a compass pointer at P and length equal to CD , draw an arc on the line, say this point as Y.
(5) Now XY is the required line.
Ques- Draw a line segment PQ = 6.2 cm. Draw the perpendicular bisector of PQ. (4 marks)
Ans-
- Draw a line segment PQ = 6.2 cm.
- Keep P as the center and take the radius more than half of PQ, draw arcs, one on each side of PQ.
- Keeping Q as the center and taking the similar radius as before, draw arcs cutting the previously drawn arcs at A and B, respectively.
- Draw AB, meeting PQ at R.
Ques- Draw a line AB. Take a point P outside it. Draw a line passing through P and perpendicular to AB. (4 marks)
Ans-
- Draw a line AB.
- Take a point P outside AB.
- With P as the center and a convenient radius, draw an arc intersecting AB at M and N, respectively.
- Draw an arc keeping M as the center and radius more than half of the MN line segment.
- With N at the center and similar radius, draw an arc cutting the previously drawn arc at Q.
- Draw PQ meeting AB at S.
PQ is the line passesing through P and is perpendicular to AB.
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