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Medians and Centroid Theorem by Tim Brzezinski

Medians and Centroid Theorem by Tim Brzezinski
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2015-08-10 10:24
TriangleCoordinate GeometryGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems Triangles: Points of Concurrency
This applet demonstrates the medians and centroid of a triangle. By constructing a triangle and drawing its medians, students can visually understand the median theorem and properties of the centroid. The construction uses Segment, Midpoint, Intersect, and Polygon commands. Suitable for middle school and above students learning triangle geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_1
  2. Segment(B, C) → b_1
  3. Midpoint(a_1) → E_1
  4. Midpoint(b_1) → F_1
  5. Segment(C, E_1) → d_1
  6. Segment(A, F_1) → e_1
  7. Intersect(d_1, e_1) → G
  8. Segment(C, G) → c
  9. Segment(G, E_1) → d
  10. Segment(A, G) → a
  11. Segment(G, F_1) → b
  12. Segment(B, G) → e
  13. Midpoint(A, C) → E
  14. Midpoint(C, B) → D
  15. Midpoint(B, A) → F
  16. Segment(A, E) → c_1
  17. Segment(E, C) → f_1
  18. Segment(C, D) → l
  19. Segment(D, B) → m
  20. Segment(B, F) → n
  21. Segment(F, A) → p
  22. Segment(G, E) → f
  23. Segment(C, F) → g
  24. Segment(A, D) → h
  25. Segment(B, E) → i
  26. Midpoint(C, G) → H
  27. Midpoint(A, G) → I
  28. Midpoint(B, G) → J
  29. Segment(C, H) → k_1
  30. Segment(H, G) → l_1
  31. Segment(G, F) → m_1
  32. Segment(A, I) → n_1
  33. Segment(I, G) → p_1
  34. Segment(G, D) → q_1
  35. Segment(B, J) → r_1
  36. Segment(J, G) → s_1
  37. Segment(G, E) → t_1
  38. Polygon(A, B, C) → poly1, c_2, a_2, b_2

AI Drawing Prompt Reference

Draw a triangle and its three medians to demonstrate their intersection at the centroid. Start by plotting three vertices and connecting them to form the sides. Then, find the midpoint of each side and draw lines from the vertices to these midpoints to create the medians. Finally, identify the point where the medians intersect, which is the centroid, and observe that it divides each median into a 2:1 ratio.
The prompt above was compiled from the original drawing commands and is for reference only.