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2.9 – Medians and Altitudes


  • Explore the medians and altitudes of triangles.
  • Discover the centroids, orthocenters, incenters, and circumcenters of triangles.


Key Terms

  • Altitude of a Triangle – The line segment from a vertex of a triangle that is perpendicular to the opposite side.
    • The altitude is sometimes OUTSIDE of the triangle
    • The altitude is sometimes ON the triangle’s side (right triangles)

GeoA 2.09 - Altitude


  • Median of a triangle – A line or segment joining a vertex of a triangle to the midpoint of the opposite side.
    • In the example below, the median passes through vertex A and bisects side \overline{BC}.

GeoA 2.09 - Medians

  • Orthocenter – The point at which the three altitudes of a triangle intersect.
    • The othercenter is found (the purple dot in the image below):
      • Inside acute triangles
      • Outside obtuse triangles
      • On the vertex of a the right angle for right triangles


  • Centroid of a triangle – The point at which the three medians of a triangle intersect.
    • The centroid of any triangle is ALWAYS INSIDE the triangle
    • How to Find the Centroid of a Triangle:
      • Step 1: Find the midpoint of one side.
      • Step 2: Draw a segment connecting the midpoint to its opposite vertex.
      • Step 3: Repeat steps 1 and 2 for the other two sides.
      • Step 4: The point where the three segments intersect is the centroid

GeoA 2.09 - Centroid



Altitudes and Medians
  • Altitudes form orthocenters
  • Medians form centroids

GeoA 2.09 - Definitions GeoA 2.09 - Centroid1 GeoA 2.09 - Orthocenter2

  • Isosceles Triangles have dividing lines that are both: medians and altitudes

GeoA 2.09 - Isosceles01

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