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Right Triangle Relationship

Right Triangle Relationship
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2020-04-03 04:35
TrianglePolygonCoordinate Geometry
This example demonstrates the relationship between the Pythagorean Theorem and the area of a right triangle. It involves key concepts of right triangles, using multiple geometric objects such as polygons, points, and distances to visually illustrate the properties of right triangles. Suitable for middle school and above students to learn geometric construction and the Pythagorean Theorem.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c_1, a_1, b_1
  2. Polygon(C, A, 4) → poly1, f, g, h, i, D, E
  3. Polygon(A, B, 4) → poly2, j, k, l, m, F, G
  4. Polygon(B, C, 4) → poly3, n, p, q, r, H, I
  5. PointIn(poly3) → Pointpoly3_1
  6. PointIn(poly3) → Pointpoly3_2
  7. PointIn(poly3) → Pointpoly3_3
  8. PointIn(poly2) → Pointpoly2_1
  9. PointIn(poly1) → Pointpoly1_1
  10. PointIn(poly2) → Pointpoly2_2
  11. Perimeter(t1) → perimetert1
  12. PointIn(t1) → Pointt1
  13. Angle(C, A, B) → α
  14. Rotate(B, 90°, A) → B'
  15. Rotate(B, (-(90°)), A) → B'_1
  16. Angle(B'_1, A, B) → β
  17. PointIn(poly3) → Pointpoly3
  18. PointIn(poly2) → Pointpoly2
  19. PointIn(poly1) → Pointpoly1
  20. Distance(B, c_1) → distanceBc1

AI Drawing Prompt Reference

Draw a right triangle ABC, then construct equilateral triangles outside each side of the right triangle. Next, select a point inside each equilateral triangle, calculate the perimeter and area of the right triangle, and label the angles of the two acute angles in the right triangle.
The prompt above was compiled from the original drawing commands and is for reference only.