GeoGebra Geometric Construction: Pyramid and Circle

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2015-02-20 12:13

This example demonstrates how to construct a pyramid and a circle using GeoGebra tools. The key mathematical concepts include geometric construction, properties of circles, and polygon creation. The construction involves commands like PointIn, Polygon, OrthogonalLine, Point, Vector, Translate, Intersect, and Plane, along with objects such as points, vectors, and planes. It is suitable for middle or high school students for learning solid geometry and coordinate geometry, suitable for classroom demonstrations or self-study.

GeoGebra Commands & Parameters

PointIn(a) → A
PointIn(a) → B
PointIn(a) → C
Polygon(A, B, C) → poly1, c, a_1, b
OrthogonalLine(C, a) → d
Point(d) → D
Vector(C, D) → u
Translate(poly1, u) → poly1'
Polygon(C, D, A) → poly2, a_2, c_1, d_1
Polygon(D, B, C) → poly3, c_2, d_2, b_1
Polygon(A, B, D) → poly4, d_3, a_3, b_2
PointIn(poly1') → E
PointIn(poly1') → F
Polygon(E, A, F) → poly5, f, e, a_4
Polygon(A, D, E) → poly6, e_1, a_5, d_4
Polygon(F, D, A) → poly7, a_6, f_1, d_5
Polygon(F, B, A) → poly8, a_7, f_2, b_3
Polygon(F, D, B) → poly9, b_4, f_3, d_6
Polygon(D, A, F) → poly10, f_4, d_7, a_8
Intersect(a_2, c_1) → G
Plane(B, C, G) → j
Plane(F, A, B) → k

AI Drawing Prompt Reference

Draw a triangle defined by three points, then construct a perpendicular line from one vertex to the opposite side to find the foot of the perpendicular. Use the triangle as a base and the foot of the perpendicular as the apex to form a tetrahedron. Randomly select points on each side of the base triangle, connect these points to create new polygons, and finally form a complex geometric solid.

The prompt above was compiled from the original drawing commands and is for reference only.