5.10Coordinate Proofs with Triangles
Quick Answer
A coordinate proof places a triangle on the coordinate plane with strategic vertex placement, then uses the distance formula, midpoint formula, and slope to verify geometric properties algebraically.
Essential Question
How does placing a triangle on the coordinate plane allow us to prove geometric properties using algebra?
Learning Goals
- 1Place a triangle strategically on the coordinate plane.
- 2Use the distance formula to verify side lengths.
- 3Use the midpoint formula to verify midpoints and midsegments.
- 4Use slope to verify perpendicularity or parallelism.
- 5Write a complete coordinate proof.
Key Vocabulary
Coordinate proof
A proof that uses coordinates and algebraic formulas to verify geometric properties.
Strategic placement
Positioning a figure on the coordinate plane to simplify calculations (e.g., placing one vertex at the origin).
Full lesson content coming soon
Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.