Copy a supplied segment or angle with a compass
Transfer a segment length without measuring it · Copy an angle using equal arcs and a chord · Leave evidence of the construction
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Segments, rays and angles
- Accurate compass handling
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Transfer a segment length without measuring it
- Copy an angle using equal arcs and a chord
- Leave evidence of the construction
Prepare your paper
When a practice task gives numerical input geometry rather than a printed figure, first prepare that source segment, angle, triangle or circle with measuring tools as needed. Then put the measuring scale or protractor aside for the requested formal copying or bisector steps: use a compass and unmarked straightedge to locate the new points. The preparation supplies the givens; it is not a replacement for the formal construction.
The website diagrams explain relationships; their screen size is not a centimetre calibration or a ready-to-measure template. Keep the input figure and useful construction arcs on paper. Your drawing is self-checked and needs human review for reliable marking.
Copy a segment
Start with the supplied segment AB and a new ray from P. Set the compass opening to the distance AB directly. Without changing the opening, draw an arc centered at P to meet the ray at Q. The copied segment PQ equals AB. An unmarked straightedge draws the ray; a ruler measurement is not the formal copying method.
Copy an angle
For a supplied non-reflex angle with vertex O, draw an arc centered at O meeting its arms at A and B. With the same radius draw an arc at the new vertex P, meeting its starting ray at D. Set the compass to chord AB; an arc centered at D meets the new P-arc at E on the chosen side. Draw PE: angle DPE copies angle AOB.
The equal radii and equal chord produce congruent triangles, justifying the copied angle. Choose the correct side and orientation; if a reflex turn is specified, identify that turn rather than confusing it with the smaller angle between the same rays. Leave useful arcs visible. These paper constructions are self-checked, not automatically marked.
Sources for this lesson
Pause and explain
When copying an angle, what is transferred after the equal-radius arcs?
Worked example
Copy a supplied 6 cm segment AB onto a ray from P.
Show the worked solution
- Set the compass opening directly from A to B.
- Draw a P-centered arc crossing the ray at Q; draw or identify PQ.
- Check PQ = AB without using measurement to locate Q.
Answer PQ is a 6 cm copy; the compass arc shows how Q was fixed.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Copy a supplied 4.8 cm segment onto a given ray. Describe the construction and evidence.
Give me a hint
Transfer the given distance with the compass.
Compare my reasoning
- Set the opening to the supplied segment.
- Draw an arc from the ray's endpoint to locate the new endpoint; keep the arc.
A 4.8 cm copy on the ray, located by the unchanged compass opening.
Look for these in your work
- Use the supplied distance
- Retain the locating arc
Copy a supplied 70° non-reflex angle onto a new starting ray without using a protractor to locate its second arm.
Give me a hint
Use equal-radius arcs and their chord.
Compare my reasoning
- Draw matching arcs at the original and new vertices.
- Transfer the original arc chord to locate E on the new arc; draw the second arm on the intended side.
A copied 70° angle, justified by equal radii and equal chord.
Look for these in your work
- Transfer the chord as well as the radius
- Choose the correct orientation
A student draws matching arcs at two vertices but chooses any point on the second arc. Is the angle necessarily copied? Explain how to repair it.
Give me a hint
Ask which distance fixes the separation of the arms.
Compare my reasoning
- No: the chord between the two intersections has not been fixed.
- Transfer the original chord with an arc from the new starting intersection, then join the new vertex to that located point.
Not necessarily. Transfer the chord to determine the second arm.
Look for these in your work
- Identify the missing condition
- Give a constructive correction
Common mistakes
- Do not change the compass opening during a transfer.
- Equal radii alone do not copy an angle; the chord must be transferred too.
What can you explain now?
When copying an angle, what is transferred after the equal-radius arcs?
Compare with the explanation
The chord between the original arc's two arm intersections.
That third equal side fixes the new angle, rather than just its radius.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
When copying an angle, what is transferred after the equal-radius arcs?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.