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Similar Triangles SAS Construction and Properties

Similar Triangles SAS Construction and Properties
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2018-09-24 21:21
TriangleTransformationGeometric Construction
This example demonstrates the construction of similar triangles using the SAS (Side-Angle-Side) criterion and illustrates their geometric properties. The key mathematical concepts include the criteria for similarity, proportional relationships, and construction steps. The construction involves GeoGebra commands such as Rotate, Polygon, IntersectPath, using objects like BLviewBox, D, A, etc. This example is suitable for middle or high school mathematics teaching to understand the basic principles of similar triangles and construction techniques.

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