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Pythagoras Motorway Problem

Pythagoras Motorway Problem
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2015-02-09 01:33
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the application of the Pythagorean Theorem in a motorway problem. Key mathematical concepts include the Pythagorean Theorem and geometric construction. Using GeoGebra commands such as Segment, Point, Distance, and Midpoint, a geometric model of the motorway can be constructed. Suitable for middle school and above students to learn and explore.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Point(a) → E
  3. Segment(C, E) → b
  4. Segment(E, D) → c
  5. Segment(C, A) → d
  6. Segment(D, B) → e
  7. Distance(c, b) → f
  8. Distance(E, B) → distanceEB
  9. Midpoint(E, B) →
  10. Distance(A, E) → distanceAE
  11. Midpoint(A, E) →

AI Drawing Prompt Reference

Draw a right triangle with points A and B as the right angle vertices, and point C on the extension of AB, and point D on the extension of BC. Use the segment tool to connect A and B, B and C, and C and D. Then select the midpoint E on AB, and connect E to C and D. Measure the lengths of segments CD and BE, as well as the distance from A to E.
The prompt above was compiled from the original drawing commands and is for reference only.