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Cosine Relationship in Isosceles Triangle

Cosine Relationship in Isosceles Triangle
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2021-12-21 21:30
TriangleTrigonometryGeometric Construction
In collections Open Middle: Distance, Midpoint, Slope (2)
This example demonstrates the application of the cosine theorem in isosceles triangles. Key mathematical concepts include isosceles triangles and the cosine theorem. Using GeoGebra commands such as PointIn, Segment, and Midpoint, an isosceles triangle can be constructed and its angles and side lengths calculated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. PointIn(e) → A
  2. PointIn(e) → B
  3. PointIn(e) → C
  4. Textfield(f) → InputBox1
  5. Textfield(g) → InputBox2
  6. Textfield(h) → InputBox3
  7. Textfield(i) → InputBox4
  8. Textfield(j) → InputBox5
  9. Segment(A, B) → k
  10. Midpoint(k) → D
  11. Segment(A, D) → l
  12. Segment(D, B) → m
  13. Intersect(p, eq1) → E
  14. Polygon(A, E, B) → t1, b_1, a_1, e_1
  15. Angle(B, E, A) → α
  16. Segment(A, E) → n
  17. Segment(E, B) → q
  18. If(C ≟ D, "√", "X") → text6
  19. Mode(l1) → l2
  20. If(c2, "√", "X") → text8
  21. If(c3, "√", "X") → text9
  22. If(Length[l2] ≟ 0, "No digits repeat!", "Repeated digits exist.") → text7

AI Drawing Prompt Reference

Draw an isosceles triangle in the plane: place three points to represent the triangle’s vertices, connect the two base points to form the base segment, and construct the midpoint of the base. From this midpoint, draw segments to the two base endpoints to establish the isosceles structure. Use a further segment tied to one of the equal sides to create an intersection point with the other side, which determines the third vertex position. Create the closed triangle using the three vertices, then mark the angle at the intersection with the rays going toward the other two vertices (angle BEA). Also display key edge segments so side lengths can be visually compared, and include text fields intended for showing numeric/length-related information and checks.
The prompt above was compiled from the original drawing commands and is for reference only.