What classical tools are allowed in an ideal compass-and-straightedge construction?
Unit 01 · Lesson 04 · Foundations, Constructions & Geometric Reasoning
Compass-and-Straightedge Constructions
Construct congruent segments and angles, perpendicular bisectors, angle bisectors, and perpendicular or parallel lines using classical tools.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to construct congruent segments and angles, perpendicular bisectors, angle bisectors, and perpendicular or parallel lines using classical tools.
Success evidence
- Label the figure and units before calculating.
- Select and justify the governing definition, theorem, relationship, or construction.
- Show enough work that another learner can audit the conclusion.
- Check the result against the diagram, scale, and stated constraints.
Visual model
Use definitions, measurements, constructions, and logical statements to establish a precise geometric argument.
AB=|b-a|M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)m\angle A+m\angle B=180^\circ
Worked reasoning
Process: State what is given, translate each fact into a definition or theorem, and justify every conclusion in order.
- Read the figure and rewrite all given information with correct notation.
- Identify the exact relationship that connects the known and unknown quantities.
- Substitute, construct, or prove one justified step at a time.
- State the result with units and a sentence explaining what it means.
Misconception check: A diagram suggests relationships, but only stated markings, definitions, and proven results may be used as evidence.
Khaemenes Academy · Open-Age Geometry
Compass-and-Straightedge Constructions
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
What locus is created by the perpendicular bisector of segment AB?
Name the first arc step when copying an angle.
Why must construction arcs remain visible in a proof-quality drawing?
What construction divides an angle into two congruent angles?
Can a general angle be trisected with classical compass and straightedge?