Four Triangle Centers
About This MicroSim
This interactive visualization shows all four classical triangle centers in a single view, allowing direct comparison of their positions and behaviors as the triangle shape changes.
The Four Centers
| Center | Symbol | Defined By | Special Property |
|---|---|---|---|
| Centroid | G | Medians | Balance point; always inside |
| Circumcenter | O | Perpendicular bisectors | Equidistant from vertices |
| Orthocenter | H | Altitudes | On Euler line |
| Incenter | I | Angle bisectors | Equidistant from sides; always inside |
Key Relationships
The Euler Line
When all centers are visible, notice the Euler line (dashed brown) connecting: - G (Centroid) - O (Circumcenter) - H (Orthocenter)
The incenter (I) generally does NOT lie on the Euler line (except in isosceles triangles).
Location Behavior
- G and I: Always inside the triangle
- O: Inside (acute), on hypotenuse (right), outside (obtuse)
- H: Inside (acute), at right-angle vertex (right), outside (obtuse)
Interactions
- Drag vertices to reshape the triangle
- Click buttons to toggle individual centers on/off
- Watch how center positions change with triangle type
Learning Objectives
- Compare the four classical triangle centers
- Recognize which centers lie on the Euler line
- Understand how center locations depend on triangle type
Bloom's Taxonomy Level
Analyzing and Evaluating