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Hypotenuse is the Longest Side in a Right Triangle

Hypotenuse is the Longest Side in a Right Triangle
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2015-03-10 05:17
TriangleAngleGeometric Construction
This example dynamically demonstrates the side lengths of a right triangle to help students discover and verify that the hypotenuse is the longest side. It uses GeoGebra commands such as Intersect, Point, Segment, Circle, and OrthogonalLine for construction. Suitable for middle school and above students to learn geometric construction and properties of right triangles.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Segment(B, D) → c
  4. Intersect(c, xAxis) → C
  5. Point(Circle[C, side_a]) → E
  6. Segment(C, E) → a
  7. Point(a) → F
  8. Circle(F, side_b) → d
  9. OrthogonalLine(F, a) → b
  10. Intersect(d, b, 2) → G
  11. Segment(F, G) → e
  12. Point(a) → H
  13. Circle(H, G) → f
  14. Segment(H, G) → g
  15. Point(f) → Move_1
  16. Segment(Move_1, H) → h
  17. Angle(G, F, H) → α
  18. Circle(G, H) → k
  19. Point(k) → Move
  20. Segment(G, Move) → i

AI Drawing Prompt Reference

Draw a right triangle to dynamically demonstrate the lengths of its sides, proving the hypotenuse is the longest. Start with the intersection of coordinate axes, then determine the right-angle vertex, and draw the two legs and the hypotenuse. Next, draw a circle with the legs as diameters, connect the intersection points to form the third side. Finally, label the angles and key points to complete the geometric proof.
The prompt above was compiled from the original drawing commands and is for reference only.