Centers of Triangles: Bisectors, Medians, Altitudes & Inequalities
Shared by A STEM Educator
Students will classify and construct angle bisectors, perpendicular bisectors, medians, and altitudes in triangles; identify their points of concurrency (incenter, circumcenter, centroid, orthocenter); apply the centroid ratio theorem; and use triangle inequality to determine valid side lengths and angle-side relationships.
Lesson Overview
Students progress from identifying basic segment types in triangles to applying concurrency theorems and triangle inequality reasoning, building conceptual understanding through collaborative vertical-surface work.
Materials
- Vertical whiteboards or chart paper
- Dry-erase markers (multiple colors)
- Rulers and protractors
- Random grouping tool
- Printed coordinate grids (optional)
Scaffolded Task Progression
- Aliya says is a median because is the midpoint of .
- Ben says is an altitude because it looks perpendicular.
- Carla says is an angle bisector because it splits .
For each claim, state what ONE piece of evidence you would need to confirm or deny it.
[ Interactive graph / diagram, available in the full lesson ]
Then identify: does also appear to be an altitude? Justify using slope.
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