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Perpendicular Median

Perpendicular Median
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2017-10-23 19:51
TriangleAngleCoordinate GeometryGeometric ConstructionSlider Animation
In collections SOME SPECIAL POINTS IN TRIANGLE
This example demonstrates the perpendicular median in a triangle. A perpendicular median is a line from the midpoint of one side of a triangle to the opposite vertex. The core mathematical concepts involved include the midpoint, perpendicular lines, and angles. Using GeoGebra commands such as Polygon, LineBisector, Intersect, and Angle, this construction can be created. Suitable for middle school and above students to learn triangle properties and geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → çokgen1, c, a, b
  2. LineBisector(c) → f
  3. LineBisector(b) → g
  4. LineBisector(a) → h
  5. Intersect(f, g) → D
  6. Intersect(f, a) → E
  7. Intersect(f, c) → F
  8. Angle(B, F, E) → α
  9. Intersect(g, b) → G
  10. Intersect(h, a) → H
  11. Intersect(g, a) → I
  12. Intersect(h, c) → J
  13. Angle(C, H, J) → β
  14. Angle(I, G, C) → γ

AI Drawing Prompt Reference

Draw a triangle ABC, then find the perpendicular bisectors of sides BC, AC, and AB, which intersect at points D, E, and F, where D is the intersection of the perpendicular bisector of AB and AC. Measure the angle BDF, and find the intersections of the perpendicular bisectors of AC and AB with BC at points G and H, and the intersections of the perpendicular bisectors of AB and AC with BC at points I and J. Finally, measure the angles CHJ and IGC.
The prompt above was compiled from the original drawing commands and is for reference only.