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Distance Between Two Points (Pythagorean Theorem)

Distance Between Two Points (Pythagorean Theorem)
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2020-04-29 06:43
TrianglePolygonAngleCoordinate GeometryGeometric Construction
① This example demonstrates the distance between two points in a coordinate plane by constructing a right triangle and applying the Pythagorean theorem. ② Core mathematical concepts include the Pythagorean theorem, the distance formula, right triangle properties, and coordinate geometry. ③ Construction details: Using GeoGebra commands such as Line, OrthogonalLine, Intersect, Segment, Polygon, and Angle, points A, B, C, D are created to form a right triangle, with segment lengths and angle measures displayed to illustrate the relationship. ④ Suitable for middle school geometry and algebra integration, as well as high school coordinate geometry introduction, helping students visually understand the derivation of the distance formula.

GeoGebra Commands & Parameters

  1. Line(A_1, B_1) → f
  2. OrthogonalLine(A, f) → g
  3. Line(B, f) → h
  4. Intersect(g, h) → E
  5. Segment(B, A) → i
  6. Segment(B, E) → k
  7. Line(A, f) → l
  8. Polygon(A, B, 4) → poly1, m, n, p, q, C, D
  9. OrthogonalLine(C, f) → r
  10. Line(D, f) → s
  11. Intersect(r, s) → G
  12. Angle(C, D, A) → ε
  13. Angle(D, A, B) → ζ
  14. Angle(A, B, C) → η
  15. Angle(B, C, D) → θ
  16. Intersect(g, s) → F
  17. Intersect(h, r) → H
  18. Segment(G, F) → t
  19. Segment(F, E) → a
  20. Segment(E, H) → b
  21. Segment(H, G) → c
  22. Segment(G, C) → j
  23. Segment(F, D) → d
  24. Segment(E, A) → e
  25. Angle(C, G, D) → α
  26. Angle(D, F, A) → β
  27. Angle(A, E, B) → γ
  28. Angle(B, H, C) → δ

AI Drawing Prompt Reference

Draw two points on a coordinate plane and connect them with a line segment. Through one point, draw a perpendicular line to the segment, and through the other point, draw a line parallel to the original segment; these two lines intersect to form a third point, creating a right triangle. Construct the triangle using these three vertices and display the measures of its interior angles. Then, outside the triangle, construct a square with one side coinciding with a side of the triangle. From two vertices of the square, draw perpendicular and parallel lines to the original segment, obtaining new intersection points, and connect these points to form another square. Finally, label the lengths of all key segments and the measures of all relevant angles to visually demonstrate the relationship between the distance between two points and the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.