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Another Special Theorem: Part 1

Another Special Theorem: Part 1
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2016-01-23 02:36
TriangleAngleGeometric 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 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2
This example illustrates a special theorem through geometric construction. It involves angles, similar triangles, and uses GeoGebra commands such as ray, point, segment, length, orthogonal line, circle, intersection, angular bisector, etc. Users can visually understand these concepts. Suitable for middle and high school students learning geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Ray(G, H) → p
  2. Point(p) → I
  3. Segment(G, I) → q
  4. Length(q) → r
  5. Ray(A, B) → a
  6. Ray(A, C) → b
  7. OrthogonalLine(A, a) → d
  8. Circle(A, r) → e
  9. Intersect(e, d) → F_1, G_1
  10. OrthogonalLine(A, b) → g
  11. AngularBisector(C, A, B) → s
  12. Intersect(e, g, 2) → D
  13. Line(C, g) → f
  14. Line(D, b) → i
  15. Intersect(s, i) → E
  16. Distance(E, b) → distanceEb
  17. Distance(E, a) → distanceEa
  18. Ray(A, E) → c
  19. OrthogonalLine(E, a) → h
  20. OrthogonalLine(E, b) → j
  21. Intersect(h, a) → F
  22. Intersect(j, b) → J
  23. Segment(E, F) → k
  24. Segment(E, J) → l
  25. Angle(E, J, A) → α
  26. Angle(A, F, E) → β

AI Drawing Prompt Reference

Draw a triangle ABC, and construct two rays AB and AC from point A. Draw a circle with center A and radius equal to the length of AI, intersecting the perpendiculars to AB and AC at points F and G, respectively. Construct the angle bisector of ∠BAC, which intersects the circle at point D. Draw a perpendicular from D to AC and another perpendicular from D to AB, intersecting at point E. Measure the distances from E to AB and AC, and draw circles with center E and these distances as radii, intersecting AB and AC at points F and J, respectively. Connect points E, F and E, J to form line segments EF and EJ. Measure the angles ∠FEA and ∠EFA.
The prompt above was compiled from the original drawing commands and is for reference only.