Constructing a Line Segment
In geometry, construction means drawing shapes accurately using specific tools — mainly a ruler and a compass.
The simplest construction is drawing a line segment of a given length. You can also copy a line segment (draw one equal to a given segment) using a compass.
In Class 6 Practical Geometry, you will learn both methods — using a ruler alone, and using a ruler with a compass.
What is Constructing a Line Segment - Grade 6 Maths (Practical Geometry)?
Tools needed:
- Ruler (straightedge): To draw straight lines and measure lengths.
- Compass: To transfer lengths accurately without measuring.
- Sharp pencil: For precise markings.
Two methods to draw a line segment of given length:
- Method 1: Using a ruler only.
- Method 2: Using a ruler and compass (more accurate).
Constructing a Line Segment Formula
Method 1: Using a ruler only
- Place the ruler on the paper.
- Mark a point at the 0 cm mark. Label it A.
- Mark another point at the required length (say 5.3 cm). Label it B.
- Join A and B along the ruler's edge.
- AB is the required line segment of length 5.3 cm.
Method 2: Using a ruler and compass
- Draw a line (longer than needed) using the ruler. Mark a point A on it.
- Open the compass to the required length by placing the metal tip on 0 and the pencil tip on the required measurement (say 5.3 cm) on the ruler.
- Without changing the compass opening, place the metal tip on point A.
- Draw an arc cutting the line. Label the point where the arc meets the line as B.
- AB is the required line segment.
Copying a line segment (using compass):
- You are given a line segment PQ. You need to draw another segment of the same length.
- Draw a line and mark a point A on it.
- Open the compass and place tips on P and Q (to capture the length of PQ).
- Without changing the opening, place the metal tip on A and draw an arc on the line. Mark the intersection as B.
- AB = PQ.
Types and Properties
Why use a compass instead of just a ruler?
- A ruler can have slight errors because of thick markings or the way you look at it (parallax error).
- A compass transfers lengths more accurately because the distance between the two tips is exact.
- In formal geometry constructions, the compass method is preferred.
Important tips:
- Always use a sharp pencil in the compass for clear marks.
- Do not change the compass opening once set — hold it carefully.
- Arcs should be thin and clear, not thick scribbles.
- Label all points with capital letters.
Solved Examples
Example 1: Drawing a 6 cm Line Segment with Ruler
Problem: Draw a line segment AB of length 6 cm using a ruler.
Solution:
- Place the ruler on paper.
- Mark point A at the 0 mark.
- Mark point B at the 6 cm mark.
- Join A and B along the ruler.
Answer: AB = 6 cm.
Example 2: Drawing 4.5 cm with Compass
Problem: Construct a line segment PQ of length 4.5 cm using a ruler and compass.
Solution:
- Draw a line l. Mark a point P on it.
- Open compass to 4.5 cm using the ruler.
- With metal tip on P, draw an arc on line l. Mark intersection as Q.
Answer: PQ = 4.5 cm.
Example 3: Copying a Line Segment
Problem: Given a line segment MN, construct a copy of it without measuring its length.
Solution:
- Draw a line l. Mark a point A on it.
- Open compass with tips on M and N.
- Without changing the opening, place metal tip on A and draw an arc on line l. Mark intersection as B.
Answer: AB = MN (exact copy).
Example 4: Constructing a Sum of Two Segments
Problem: Line segment AB = 3 cm and CD = 4 cm. Construct a line segment of length AB + CD = 7 cm.
Solution:
- Draw a line. Mark point P.
- Open compass to 3 cm. From P, mark point Q on the line (PQ = 3 cm).
- Open compass to 4 cm. From Q, mark point R on the line (QR = 4 cm).
Answer: PR = 3 + 4 = 7 cm.
Example 5: Constructing a 7.8 cm Segment
Problem: Construct XY = 7.8 cm.
Solution:
- Draw a line. Mark point X.
- Set compass to 7.8 cm on the ruler.
- From X, draw an arc on the line. Label intersection as Y.
Answer: XY = 7.8 cm.
Example 6: Constructing a Difference of Segments
Problem: AB = 8 cm and CD = 3 cm. Construct a segment of length AB − CD = 5 cm.
Solution:
- Draw a line. Mark point P.
- Set compass to 8 cm. From P, mark Q (PQ = 8 cm).
- Set compass to 3 cm. From Q, mark R towards P (QR = 3 cm).
Answer: PR = 8 − 3 = 5 cm.
Real-World Applications
Where constructing line segments is used:
- Engineering drawings: Every technical drawing starts with accurate line segments.
- Architecture: Floor plans require precise lengths.
- Art: Geometric art starts with measured line segments.
- Map making: Scale drawings use exact segment lengths.
- All further constructions: Triangles, quadrilaterals, and other shapes are built from line segments.
Key Points to Remember
- A line segment can be constructed using a ruler only or a ruler and compass.
- The compass method is more accurate than using just a ruler.
- To copy a segment, use a compass to transfer the length — no measurement needed.
- Always use a sharp pencil and do not change the compass opening once set.
- You can construct a sum or difference of two segments by placing arcs one after another.
- Label all points clearly with capital letters.
Practice Problems
- Draw a line segment of length 5.6 cm using a ruler.
- Construct a line segment of length 8.2 cm using ruler and compass.
- Given a line segment of some length, copy it using only a compass.
- Construct a line segment of length 3 cm + 4.5 cm = 7.5 cm by adding two segments.
- Construct a line segment of length 9 cm − 2.5 cm = 6.5 cm.
- Construct three line segments of lengths 4 cm, 5 cm, and 6 cm.
Frequently Asked Questions
Q1. Why do we use a compass to draw line segments?
A compass gives a more accurate measurement than a ruler because it transfers the exact length without any reading error (parallax). In formal geometry, compass constructions are standard.
Q2. Can I draw a line segment using only a compass?
You need a straightedge (ruler without markings, or just the edge of a ruler) to draw the straight line. The compass sets the length, but the line itself needs a straight edge.
Q3. What if my compass opening changes while drawing the arc?
Then the length will be wrong. Hold the compass firmly at the top and rotate gently. Tighten the compass screw so it does not slip.
Q4. How do I copy a line segment without knowing its length?
Place compass tips on the two endpoints of the given segment. Without changing the opening, transfer it to a new line by drawing an arc from a marked point.
Q5. What is the difference between a ruler and a straightedge?
A ruler has markings for measurement. A straightedge is just a straight edge without markings. In pure geometry, we use a straightedge, but in school, we use a ruler.
Related Topics
- Constructing Perpendicular Lines
- Constructing Angles
- Constructing Parallel Lines
- Bisecting a Line Segment
- Bisecting an Angle
- Constructing Triangles (SSS)
- Constructing Triangles (SAS)
- Constructing Triangles (ASA)
- Constructing Triangles (RHS)
- Constructing Quadrilaterals
- Constructing Special Quadrilaterals
- Triangle Construction Problems
