Unit 5 · Triangle Congruence and ProofProof-based

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.