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Special Segments in Triangles

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About This Diagram

This comprehensive visualization shows all four types of special segments in triangles along with their points of concurrency (where all three segments of each type meet).

The Four Special Segments

Segment Definition Point of Concurrency Property
Median Vertex to midpoint of opposite side Centroid (G) Balance point; divides each median 2:1
Altitude Perpendicular from vertex to opposite side Orthocenter (H) Location varies by triangle type
Perpendicular Bisector ⊥ to side at its midpoint Circumcenter (O) Equidistant from all vertices
Angle Bisector Bisects each angle Incenter (I) Equidistant from all sides

Points of Concurrency

Centroid (G)

  • Always inside the triangle
  • "Balance point" - center of mass
  • Divides each median in ratio 2:1 from vertex

Orthocenter (H)

  • Inside for acute triangles
  • On the right-angle vertex for right triangles
  • Outside for obtuse triangles

Circumcenter (O)

  • Center of the circumscribed circle (passes through all vertices)
  • Equidistant from all three vertices

Incenter (I)

  • Always inside the triangle
  • Center of the inscribed circle (touches all sides)
  • Equidistant from all three sides

Interaction

Click on any panel to highlight it and dim the others. Click again to show all panels.

Learning Objectives

  • Identify medians, altitudes, perpendicular bisectors, and angle bisectors
  • Locate their points of concurrency
  • Understand the special properties of each center

Bloom's Taxonomy Level

Understanding, Applying, and Analyzing

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