New Pythagorean Theorem - Complex Shapes
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This example demonstrates the application of the new Pythagorean theorem in complex shapes. Key mathematical concepts include geometric transformations, similar triangles, and geometric mean. Using GeoGebra commands such as Circle, Point, Line, Intersect, etc., complex geometric shapes can be constructed. Suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
Circle(A, a) → cPoint(c) → CLine(C, A) → fIntersect(c, f, 2) → DPoint(c) → BSegment(B, C) → gPoint(f) → ERotate(E, 90°, C) → E'Point(f) → FSegment(B, D) → hPolygon(D, B, 3) → poly1, i, j, k, GPolygon(B, C, 3) → poly2, l, m, n, HPolygon(C, D, 3) → poly3, p, q, r, IPolygon(G, B, 4) → poly4, s, t, b, d, J, KPolygon(H, C, 4) → poly5, e, f_1, g_1, h_1, L, MPolygon(I, D, 4) → poly6, i_1, j_1, k_1, l_1, N, OPolygon(M, L, 3) → poly7, m_1, n_1, p_1, PPolygon(K, J, 3) → poly8, q_1, r_1, s_1, QPolygon(O, N, 3) → poly9, t_1, a_1, b_1, RPolygon(Q, J, B, D, G, K) → poly10, q_2, j_2, b_2, d_1, g_2, k_2Polygon(B, H, M, P, L, C) → poly11, b_3, h_2, m_2, p_2, l_2, c_1Polygon(D, N, R, O, I, C) → poly12, d_2, n_2, r_2, o, ı, c_2PointIn(poly10) → Pointpoly10_1PointIn(poly11) → Pointpoly11_1PointIn(poly12) → Pointpoly12_1Perimeter(poly10) → perimeterpoly10PointIn(poly10) → Pointpoly10Perimeter(poly11) → perimeterpoly11PointIn(poly11) → Pointpoly11Perimeter(poly12) → perimeterpoly12PointIn(poly12) → Pointpoly12
AI Drawing Prompt Reference
Draw a complex geometric shape with multiple triangles and quadrilaterals. Start by drawing a circle, then take point C on the circle and draw a line f through C, intersecting the circle at points B and D. Rotate point E to get E', and draw line segment BG. Construct several triangles and quadrilaterals, such as triangle BCD and quadrilateral GBDH, and finally calculate and display the perimeter of each quadrilateral.
The prompt above was compiled from the original drawing commands and is for reference only.