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Given side, height & median: Self-check applet

Given side, height & median: Self-check applet
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2016-09-16 02:16
TriangleCoordinate GeometryGeometric Construction
In collections Triangle Constructions
This example demonstrates constructing a triangle given the side length, height, and median. Key mathematical concepts include basic properties of triangles and geometric construction. It uses Segment, Midpoint, Circle, OrthogonalLine, Intersect, and Polygon commands in GeoGebra. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(X, Y) → Y_1
  3. Segment(W, Z) → g
  4. Midpoint(f) → C
  5. Circle(C, Y_1) → c
  6. OrthogonalLine(A, f) → h
  7. Circle(A, g) → d
  8. Intersect(d, h, 2) → D
  9. OrthogonalLine(D, h) → i
  10. Intersect(c, i, 2) → E
  11. Polygon(A, B, E) → target, e, a, b

AI Drawing Prompt Reference

Construct a triangle given one side length, height, and median. First, draw side AB, then find its midpoint C and draw a circle c with C as the center and the height as the radius. Next, draw a perpendicular line h from A to AB, and draw a circle d with A as the center and the median length as the radius. The intersection D of circles c and d is the vertex opposite AB. Draw a perpendicular line i from D to h, and the intersection E of i and c is the third vertex. Finally, connect A, B, and E to form triangle ABE.
The prompt above was compiled from the original drawing commands and is for reference only.