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Orthocenter Explorer

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About This MicroSim

This interactive visualization demonstrates the orthocenter of a triangle - the intersection point of the three altitudes. The orthocenter has fascinating properties related to triangle type and lies on the famous Euler line.

Key Concepts

Altitudes

An altitude is a line segment from a vertex perpendicular to the opposite side (or its extension). Every triangle has exactly three altitudes.

The Orthocenter (H)

  • The orthocenter is where all three altitudes meet
  • Its location depends dramatically on triangle type:
  • Acute triangle: Inside the triangle
  • Right triangle: At the vertex of the right angle
  • Obtuse triangle: Outside the triangle

Properties

  • The orthocenter lies on the Euler line
  • In a right triangle, H coincides with the right-angle vertex
  • The reflection of H over each side lies on the circumcircle

Interactions

  • Drag vertices A, B, or C to reshape the triangle
  • Watch how the orthocenter dramatically moves as the triangle type changes
  • Observe the right angle markers at each altitude foot

Learning Objectives

  • Understand that altitudes are perpendicular to opposite sides
  • Identify the orthocenter as the intersection of altitudes
  • Recognize how orthocenter location varies with triangle type
  • Connect the orthocenter to special triangle properties

Bloom's Taxonomy Level

Understanding and Analyzing