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Similar Triangles AA Similarity Interactive Practice (MT3-02-P2a-XT1)

Similar Triangles AA Similarity Interactive Practice (MT3-02-P2a-XT1)
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2018-09-24 21:19
TriangleAngleTransformationGeometric ConstructionSlider Animation
① This GeoGebra example is an interactive exercise that demonstrates and checks whether two triangles are similar by the AA (Angle-Angle) criterion, providing immediate feedback. ② The core mathematical concept is the AA similarity theorem: if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar and their corresponding sides are proportional. ③ Construction highlights: using GeoGebra commands such as Rotate, Polygon, IntersectPath, Line, Point, Intersect, Angle, If, and LaTeX to build draggable triangles, measure angles, implement conditional logic for feedback, and include a checkbox (checkbox1) to toggle auxiliary lines or similarity marks, plus a 'TryAnother' button to generate new problems. ④ Suitable for middle school geometry teaching or self-study, to reinforce the AA similarity condition, and useful as an interactive classroom activity or formative assessment tool.

GeoGebra Commands & Parameters

  1. Rotate(D, α, A) → D'
  2. Polygon(BLviewBox, (x(BLviewBox), y(TRviewBox)), TRviewBox, (x(TRviewBox), y(BLviewBox))) → viewBox, vbLeft, vbTop, vbRight, vbBottom
  3. IntersectPath(Ray[A, D'], viewBox) → BPath_1
  4. UnicodeToLetter(10007) → xmark
  5. UnicodeToLetter(10003) → cmark
  6. Line(B, C) → f
  7. Point(BPath_1) → B'
  8. Line(B', f) → g
  9. Intersect(Ray[A, D], g) → C''
  10. Polygon(A, B, C) → tABC, c, a, b
  11. Point(Segment[A, (x(TRviewBox), y(A))]) → C'
  12. Line(C', f) → h
  13. Intersect(h, Ray[A, D']) → B''
  14. Polygon(A, B'', C') → tSimilarC, tSimilarC_c, tSimilarC_a, tSimilarC_b
  15. Polygon(A, B', C'') → tSimilarB, tSimilarB_c, tSimilarB_a, tSimilarB_b
  16. Point(Segment[A, Intersect[Ray[A, B], viewBox]]) → Bfree
  17. Point(Segment[A, (x(TRviewBox), y(A))]) → Cfree
  18. Polygon(A, Bfree, Cfree) → tFree, tFree_c, tFree_a, tFree_b
  19. LaTeX(If[bActive, "\(C'\)", "\(B'\)"]) → inactivePoint
  20. If(¬displaySimilar, Bfree, If[bActive, B', B'']) → BlblPos
  21. If(¬displaySimilar, Cfree, If[bActive, C'', C']) → ClblPos
  22. Angle(A, B, C) → angleABC
  23. Angle(B, C, A) → angleBCA
  24. Angle(C, A, B) → angleCAB
  25. Angle(A, B', C'') → angleAB'C'_b
  26. Angle(A, B'', C') → angleAB'C'_C
  27. Angle(B', C'', A) → angleB'C'A_B
  28. Angle(B'', C', A) → angleB'C'A_C

AI Drawing Prompt Reference

An interactive geometry exercise that demonstrates the AA (Angle‑Angle) similarity criterion for two triangles. The figure shows a fixed reference triangle and two draggable vertices that let the user reshape a second triangle. The three interior angles of both triangles are measured and displayed in real time, and the app instantly indicates whether the two angles match, highlighting the proportional sides when they do. A checkbox toggles auxiliary construction lines or similarity marks, and a “Try Another” button generates a new random triangle for further practice. The layout is clean and suited for middle‑school geometry lessons or self‑study.
The prompt above was compiled from the original drawing commands and is for reference only.