How to Construct a Copy of a Line Segment Using Compass and Ruler
Geometrical Construction
Geometrical construction is all about drawing lines, angles, and different shapes using pen, pencil, straight edge, protractor and a compass. A compass is a geometrical drawing instrument used for drawing circles and arcs. A straightedge, such as a ruler, is used to draw line segments. You can use a compass and a straightedge to construct basic geometric figures. You know a line segment is a line with two endpoints. Line segments that have the same length i.e equal measures are called congruent segments. To draw any shape you should know how to copy line segments.In this article we will study how to copy line segments using pure construction using ruler compass step by step.
Line Segment
A line segment is defined as a part of a line which connects two points within a line. Different numbers of line segments give us different geometrical figures. A line segment is formed by two endpoints. In the figure, m is any line and AB is the line segment on the line m.
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Constructing Copy of Line Segment
The tools you will need to copy and construct any line segment of a given length, along with your pen or pencil, are a compass and a straight edge. The most common straight edge is the ruler. But you can use anything that will give you a nice clean straight line. The compass is the mathematical tool that lets you draw nice clean circles and arcs.
The construction of line segments is not accurate when we use a ruler. Hence, we can make use of a ruler-compass combination to construct a copy of line segments. This is the pure construction in maths as no measures and numbers are involved. It is necessary to draw the straight line for the given measure in order to copy it.
Steps for Pure Construction Using Ruler Compass:
PQ is a given line segment whose copy is to be constructed
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Step 1: Mark any R that will be one end point of the new segment.
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Step 2: Set the compass pointer exactly on the point P of the line segment to be copied
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Step 3: Adjust the compass such that the pointer is at P and the pencil point is at Q. The compass width is now equal to the length of the line segment PQ which is to be copied.
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Step 4: Without disturbing the compasses' width, place the compass point on the the point R on the line you drew in step 1
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Step 5: Without changing the compass width, Draw an arc roughly where the other endpoint of the segment will be.
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Step 6: Pick any point say S on the arc that will be the other endpoint of the new line segment.
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Step 7 :Draw a line from point R to point S.
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Step 8: Thus we get the line segment RS is equal in length to the line segment PQ. RS is the copy of the line segment PQ
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Proof:
The compass is considered as a measuring tool for copying the line segment. Since the original line segment and the copied line segment are of the same length, the segments are considered as congruent line segments. Therefore PQ = Rs
All the points on the arc are the same distance from R, as R is the center of the arc.
FAQs on Construction of a Copy of a Given Line Segment
1. What is construction of a copy of a line segment?
The construction of a copy of a line segment is the geometric process of drawing a new line segment equal in length to a given line segment using a compass and ruler. It ensures that the new segment has the same measurement as the original without using a scale for measurement. This is a basic concept in geometry used in constructions of triangles, parallel lines, and other figures.
2. How do you construct a copy of a line segment using a compass?
To construct a copy of a line segment, use a compass to transfer its exact length onto another line. Follow these steps:
- Draw a line and mark a point A where the new segment will start.
- Open the compass to the length of the given line segment.
- Place the compass needle on point A.
- Mark an arc on the line to locate point B.
- The segment AB is equal to the given line segment.
3. Why do we use a compass instead of a ruler to copy a line segment?
A compass is used instead of a ruler because it transfers the exact length without measuring numerically. A ruler may introduce measurement errors due to reading inaccuracies, while a compass maintains the precise distance between its two points. This makes compass constructions more accurate in geometric constructions.
4. What are the steps to construct a line segment equal to a given line segment?
The steps to construct a line segment equal to a given one are simple and systematic:
- Given a segment CD, draw a line and mark a starting point A.
- Set the compass width equal to the length of CD.
- Place the compass needle at A and draw an arc cutting the line at B.
- The segment AB = CD.
5. What tools are required for constructing a copy of a line segment?
The tools required for constructing a copy of a line segment are a compass, a ruler (straightedge), and a pencil. The ruler is used only to draw straight lines, while the compass is used to copy the exact length of the given segment. No measurement markings are required for accurate geometric construction.
6. Can you give an example of constructing a copy of a 5 cm line segment?
Yes, to construct a copy of a 5 cm line segment, follow these steps:
- Draw a line and mark point A.
- Measure 5 cm on the compass using the given segment.
- Place the compass at A and draw an arc to cut the line at B.
- The new segment AB = 5 cm.
7. What is the difference between measuring and constructing a line segment?
The difference is that measuring uses a ruler to find the numerical length, while constructing uses a compass to copy the exact distance geometrically. Measuring gives a value like 6 cm, whereas construction transfers the same length without reading numbers. Construction is more precise in geometric proofs and diagrams.
8. What are common mistakes when copying a line segment?
Common mistakes when copying a line segment include incorrect compass width and moving the compass while marking. Key errors are:
- Changing the compass opening after measuring the given segment.
- Not placing the compass needle exactly on the starting point.
- Using a ruler scale instead of compass transfer.
9. Is construction of a copy of a line segment important in triangle construction?
Yes, constructing a copy of a line segment is essential in triangle construction because it helps create sides of equal length. For example, when constructing an equilateral or isosceles triangle, equal sides are formed by copying a given segment using a compass. This ensures geometric accuracy in shape formation.
10. How do you verify that two constructed line segments are equal?
Two constructed line segments are verified as equal by comparing them with a compass. Place the compass on one segment to fix its width, then check if it fits exactly on the other segment without changing the opening. If both match perfectly, then AB = CD, confirming the segments are equal in length.
