Geometry Lesson
Proving Quadrilateral Properties Using Coordinates
Shared by A STEM Educator
High SchoolThin-SlicingCCSS.MATH.CONTENT.HSG.GPE.B.4, CCSS.MATH.CONTENT.HSG.GPE.B.5, CCSS.MATH.CONTENT.HSG.CO.C.1150 min
Learning Objective
Students will be able to use slope, distance, and midpoint formulas to classify and prove properties of quadrilaterals on the coordinate plane.
Lesson Overview
Students progress from identifying slope and distance formulas to constructing full coordinate proofs that classify quadrilaterals by their properties. Tasks build from computing a single slope to writing a structured proof that a given quadrilateral is a specific type.
Materials
- Vertical whiteboards or large chart paper
- Dry-erase markers (multiple colors)
- Rulers or straightedges
- Random grouping cards
- Printed coordinate grids (optional)
Scaffolded Task Progression
1Task 1
Four points are given: , , , .
1. Plot all four points.
2. Compute the slope of each side: , , , .
3. What do you notice about opposite sides?
1. Plot all four points.
2. Compute the slope of each side: , , , .
3. What do you notice about opposite sides?
2Task 2
Same quadrilateral: , , , .
Now check whether adjacent sides are perpendicular.
- Are and perpendicular?
- Use the slopes from Task 1 to justify your answer.
What type of quadrilateral is ?
Now check whether adjacent sides are perpendicular.
- Are and perpendicular?
- Use the slopes from Task 1 to justify your answer.
What type of quadrilateral is ?
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