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Sections of Triangular Prisms by Kalissa

Sections of Triangular Prisms by Kalissa
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2019-07-30 00:42
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the various cross-sections formed by a triangular prism. Key math concepts include prism geometry, Pythagorean theorem, line segments, intersections, derivatives, and cross-sectional area calculations. It is constructed using commands like Polygon, PointIn, Translate, Rotate, Prism, Plane, IntersectPath, and OrthogonalLine. Suitable for high school solid geometry instruction and exploratory learning.

GeoGebra Commands & Parameters

  1. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  2. PointIn(poly3) → C
  3. Translate((0, 0, 0), Vector[B, C]) → A
  4. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  5. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  6. Rotate(D, 120°, (0, 0, 0)) → E
  7. Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
  8. Prism(poly4, D + (0, 0, 4)) → m, M, edge4, edge5, edge6, N, face1, face2, face3, face4, edge1, edge2, edge3
  9. PointIn(poly2) → G
  10. PointIn(poly2) → H
  11. PointIn(poly2) → I
  12. Plane(G, I, H) → n
  13. IntersectPath(n, m) → poly6, poly5, r, a_1, b_1, c_1, K, L_1, O, P, J, L, p, q
  14. Rotate(m, 0, zAxis) → m'
  15. Rotate(m, 0, zAxis) → m'_1
  16. OrthogonalLine(A, n) → d_1

AI Drawing Prompt Reference

Draw a triangular prism to demonstrate various cross-sections. Start by creating a prism with a rectangular base and a triangular top. Then, connect a point randomly on the top face to the base to form a triangular cross-section. Next, rotate the rectangular base around the center of the top face to create another triangular cross-section. Finally, select random points within the rotated triangle, draw a plane through these points, and show the intersections with the prism to highlight different cross-sections, labeling key points and lines.
The prompt above was compiled from the original drawing commands and is for reference only.