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Right Triangle with Median as Geometric Mean

Right Triangle with Median as Geometric Mean
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2016-04-05 17:12
Triangle
This example demonstrates the phenomenon of the median in a right triangle being a geometric mean. Key mathematical concepts include geometric mean and triangle properties. It is constructed using GeoGebra commands such as Segment, Circle, Point, Ray, Intersect, AngularBisector, Polygon, etc. Suitable for middle school and above students or teachers for teaching purposes.

GeoGebra Commands & Parameters

  1. Segment(A, B) → c
  2. Circle(C, c / 2) → d
  3. Point(d) → D
  4. Ray(D, C) → a_1
  5. Intersect(d, a_1, 2) → E
  6. Circle(E, C) → e
  7. Intersect(d, e, 1) → F
  8. AngularBisector(F, C, E) → b_1
  9. Intersect(d, b_1, 2) → G
  10. Polygon(G, D, E) → poly1, a, g, b
  11. Segment(G, C) → f
  12. Angle(D, G, E) → α

AI Drawing Prompt Reference

Draw a right triangle where one median is the geometric mean. Start by drawing the two legs of the right triangle, then draw a circle with the midpoint of the hypotenuse as the center and half the hypotenuse as the radius. The intersection of the circle and the hypotenuse is one vertex of the right triangle. Draw a ray from this vertex to the midpoint of the hypotenuse, and the other intersection of the ray and the circle is the third vertex of the right triangle. Connect the three vertices to form the triangle, then draw the median and mark the angle.
The prompt above was compiled from the original drawing commands and is for reference only.