Unit 8 · Polygons and Quadrilaterals

8.8Coordinate Proofs with Quadrilaterals

Quick Answer

To prove a quadrilateral is a specific type using coordinates: use the distance formula (side lengths), slope formula (parallel/perpendicular sides), and midpoint formula (diagonal bisection).

Essential Question

How do the distance, slope, and midpoint formulas together provide all the tools needed to classify any quadrilateral in the coordinate plane?

Learning Goals

1Use slope to identify parallel and perpendicular sides.
2Use the distance formula to compare side lengths.
3Use the midpoint formula to check diagonal bisection.
4Write a coordinate proof classifying a quadrilateral.

Key Vocabulary

Coordinate proof

A proof that uses coordinates and algebraic formulas to establish geometric properties.

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.