Copying a line segment in geometry is a fundamental construction, typically performed using only a compass and a straightedge. This process allows you to create a new line segment that has the exact same length as a given segment without measuring its length numerically.
The Method Using Compass and Straightedge
The core technique for copying a line segment relies on the ability of a compass to transfer distances. Here are the steps involved:
Step-by-Step Guide
To copy a line segment, follow these steps based on standard geometric constructions and incorporating information from sources like CK-12's geometry resources:
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Start with the Original Segment: Begin with the line segment you wish to copy. Let's call this segment AB. (Referencing Step 1 from the provided information: Start with a line segment that we will copy.)
- Example: Imagine a line segment drawn on a piece of paper.
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Draw a Reference Line/Ray: Use your straightedge to draw a line or ray starting at a point where you want the copied segment to begin. This line must be longer than the segment you are copying. Let's mark the starting point as C. (Referencing Step 2 from the provided information: Mark a point that will be one endpoint of the new line segment.)
- Practical Tip: Drawing a ray ensures you have enough length to mark the copied segment.
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Measure the Original Segment's Length: Place the point of your compass on one endpoint of the original segment AB (e.g., point A). (Referencing Step 3 from the provided information: Set the compasses' point on the point of the line segment to be copied.)
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Set the Compass Width: Adjust the opening of the compass so that the pencil or drawing end rests precisely on the other endpoint of the original segment (e.g., point B). The compass width is now set to the exact length of segment AB. (Referencing Step 4 from the provided information: Adjust the compasses' width to the point . - interpreted as adjusting to the other endpoint).
- Key Concept: The compass holds the distance between A and B.
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Transfer the Length: Without changing the compass width, move the compass so its point is on the starting point C of your new line/ray.
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Mark the Second Endpoint: Draw an arc that intersects the line/ray you drew in Step 2. The point where the arc intersects the line/ray is the second endpoint of your copied segment. Let's call this point D.
- Result: The segment CD is now a copy of segment AB, meaning CD has the same length as AB.
Summary Table
| Step | Action | Tool(s) |
|---|---|---|
| 1 (Reference) | Have the original line segment (e.g., AB). | N/A |
| 2 (Reference) | Mark a starting point for the new segment (e.g., C) and draw a ray. | Straightedge |
| 3 (Reference) | Place compass point on one end of the original segment (A). | Compass |
| 4 (Reference) | Adjust compass width to the other end of the original segment (B). | Compass |
| 5 (Completion) | Place compass point on the new starting point (C). | Compass |
| 6 (Completion) | Draw an arc intersecting the ray to mark the new endpoint (D). | Compass |
This process ensures that the new segment is congruent to the original segment, a fundamental skill in geometric constructions.
