Basic Geometric Constructions
Grade 7 Geometry — Drawing with Only a Compass and Straightedge
Part 1 — Introduction: What Are Geometric Constructions?
1. What Are Geometric Constructions?
A geometric construction is a drawing made using only two tools:
- A compass (for drawing circles and arcs)
- A straightedge (an unmarked ruler — for drawing straight lines)
Key Rule: You may not measure lengths with a ruler. You may not use a protractor. This tradition goes all the way back to the ancient Greeks over 2,000 years ago!
2. The Two Allowed Tools
🔵 Compass
- Draws circles and arcs (parts of circles)
- Transfers a distance from one place to another
- The key idea: every point on a circle is the same distance from the center
📏 Straightedge
- Draws a straight line through any two points
- Has no markings — you cannot measure with it
- Can be extended as far as needed
3. Why Do Constructions Matter?
🧠 Reasoning
Develop deep geometric thinking
Develop deep geometric thinking
🔍 Understanding
Learn why properties work, not just that they work
Learn why properties work, not just that they work
📐 Proofs
Foundation for mathematical proofs
Foundation for mathematical proofs
🏗️ Applications
Used in design, engineering, and architecture
Used in design, engineering, and architecture
4. Construction vs. Drawing
| Feature | Drawing | Construction |
|---|---|---|
| Tools | Any tools (ruler, protractor, etc.) | Only compass and straightedge |
| Measurements | Can measure lengths and angles | No measurements allowed |
| Rigor | Approximate | Exact and rigorous |
| Justification | "It looks right" | "It must be right because…" |
5. Recording Your Constructions
Good Practice:
- Describe each step clearly ("From point $A$, draw an arc with radius $AB$…")
- Explain why the construction works (using congruent triangles, etc.)
- Label all points so someone else can reproduce your work