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Area Ratio of Similar Triangles

Area Ratio of Similar Triangles
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2015-12-08 21:17
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the area ratio and the square of the side length ratio of similar triangles. Key math concepts include similarity criteria and properties, area calculation, and proportional relationships. Construction involves commands like Polygon, Dilate, PointIn, Distance, and FractionText to build and analyze the geometric figures. Suitable for high school students to learn and understand the properties of similar triangles, ideal for classroom instruction or self-directed learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Dilate(B, 1 / 2, B) → B'
  3. PointIn(poly1) → Pointpoly1_1
  4. PointIn(poly1) → Pointpoly1_2
  5. Distance(B, A) → distanceBA
  6. Dilate(A, Scale, B) → D
  7. Dilate(B, Scale, B) → B'_1
  8. Dilate(C, Scale, B) → E
  9. Polygon(D, B'_1, E) → poly1', c'_1, a'_1, b'_1
  10. PointIn(poly1) → Pointpoly1
  11. PointIn(poly1') → Pointpoly1'
  12. Distance(B, D) → distanceBD
  13. FractionText(distanceBD / distanceBA) → text2
  14. FractionText(poly1' / poly1) → text3
  15. Distance(B, E) → distanceBE
  16. Distance(B, C) → distanceBC
  17. Distance(D, E) → distanceDE
  18. Distance(A, C) → distanceAC
  19. Perimeter(poly1) → perim
  20. Perimeter(poly1') → perim'
  21. FractionText(perim' / perim) → text6