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Exploring the Converse of Pythagoras Theorem: Dynamic Triangle Side-Length Inves

Exploring the Converse of Pythagoras Theorem: Dynamic Triangle Side-Length Inves
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2020-02-18 00:17
TriangleAngleInequalityGeometric ConstructionSlider Animation
① This interactive GeoGebra activity lets students choose three side lengths, construct a triangle, and observe whether it becomes right-angled, directly demonstrating the converse of the Pythagorean theorem: if a²+b²=c², then the triangle is right-angled. ② Core mathematical concepts include the Pythagorean theorem and its converse, triangle inequality, right-angle detection, and angle measurement. ③ Construction highlights: uses Point, Segment, Circle, Textfield, Dilate, Polygon, Angle, and Sort commands; three InputBoxes allow entering side lengths, buttons trigger actions, and a protractor object (protractor_1) visually measures angles; the Sort command helps identify the longest side for comparison. ④ Suitable for middle school geometry classes or self-directed exploration, enabling students to discover the converse theorem through hands-on experimentation and data analysis.

GeoGebra Commands & Parameters

  1. Point(Circle[A, l_{AB}]) → B
  2. Segment(A, B) → f
  3. Point(Circle[C, l_{CD}]) → D
  4. Segment(C, D) → g
  5. Point(Circle[E, l_{EF}]) → F
  6. Segment(E, F) → h
  7. Circle(A, 0.5) → c_A
  8. Circle(B, 0.5) → c_B
  9. Circle(C, 0.5) → c_C
  10. Circle(D, 0.5) → c_D
  11. Circle(E, 0.5) → c_E
  12. Circle(F, 0.5) → c_F
  13. Textfield(l_{EF}) → InputBox1
  14. Textfield(l_{AB}) → InputBox2
  15. Textfield(l_{CD}) → InputBox3
  16. Segment(P_1, P'_1) → n_1
  17. Dilate(Rotate[P_2, 182.472°, P_3], 1.076, P_3) → P_4
  18. Dilate(Rotate[P_2, -3.1936°, P_3], 1.0438, P_3) → P_5
  19. Circle(P_3, P_2) → c_1
  20. Polygon(P_3, P_2, P_6, P_7, P_4, P_5) → polyProtractor_1, p_1, p_2, p_3, p_4, p_5, p_6
  21. Angle(P'_1, P_1, P_2) → θ_1
  22. Sort({f, g, h}) → listsortedsegm

AI Drawing Prompt Reference

Draw three adjustable line segments, each with small circular endpoints. Place an input box beside each segment to enter its length. Sort the three segments by length and highlight the longest one. Using the longest segment as the base, attempt to construct a triangle with the other two segments, and measure its largest angle. If the largest angle is close to 90 degrees, display a right-angle marker. The overall scene is an interactive exploration for verifying the converse of the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.