Special Angles in Standard Position: Dynamic Templates (V2)-Part 2
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This example demonstrates the dynamic construction of 45-45-90 special right triangles in standard position. It involves core mathematical concepts like angles, trigonometry, and geometric constructions. Key GeoGebra commands and objects used include Mirror, Intersect, Dilate, Segment, Polygon, Rotate, Circle, Line, and CircleSector. Suitable for high school students learning about special right triangles and geometric constructions.
GeoGebra Commands & Parameters
Mirror(G, f) → G'Mirror(F, f) → F'Mirror(E, g) → E'Mirror(F, g) → F'_1Mirror(G, g) → G'_1Mirror(F', g) → F''Mirror(G', g) → G''Mirror(E, f) → E'_1Mirror(E'_1, g) → HIntersect(g, j) → IIntersect(g, i) → JIntersect(g, h) → KDilate(L, If[0 < a ≤ 1, 1 - a, 0], J) → L'Segment(L, L') → kDilate(J, If[1 < a ≤ 2, 2 - a, 0], F) → K'Polygon(L, J, F) → poly1, n, e, k_1Dilate(F, If[2 < a ≤ 3, 3 - a, 0], L) → E'_2Rotate(K, If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K'_1Rotate(K', If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K''Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_1Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_2Rotate(E, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → E'_3Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_3Rotate(K', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K''_1Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_2Rotate(L', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L''Rotate(K'', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'''_1Rotate(L'_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → QRotate(K'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → RRotate(E'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → SRotate(K'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → TRotate(K''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → URotate(L'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → VRotate(L'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → L'''Rotate(K'''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → WRotate(Q, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → Q'Rotate(R, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → R'Rotate(S, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → S'Rotate(V, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → V'Rotate(L''', If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → ZRotate(W, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → W'Rotate(T, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → T'Rotate(U, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → U'Rotate(K'_1, If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → E_1Rotate(K'', If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → K'''_2Dilate(K, If[9 < a ≤ 10, 10 - a, 0], E') → K'_4Rotate(E_1, π / 2, L) → T_1Rotate(K'''_2, π / 2, L) → U_1Rotate(K'''_2, π, L) → W_1Rotate(E_1, (3 * π / 2), L) → Z_1Rotate(K'''_2, (3 * π / 2), L) → A_2Segment(J, K') → lSegment(F, E'_2) → mRotate(L, If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L'_3Rotate(L', If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L''_1Segment(L'_3, L''_1) → k'_1Circle(L, 0.5) → d_1Rotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_4Rotate(J, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → J'Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_2Polygon(L'_4, J', F'_2) → poly1'_1, f'_2, l'_4, j'Rotate(L'_3, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → MRotate(L''_1, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → NSegment(M, N) → bRotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_5Rotate(L', If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L''_2Segment(L'_5, L''_2) → k'_3Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_3Rotate(E'_2, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → PSegment(F'_3, P) → m'Rotate(L'_4, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → ORotate(J', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → J''Rotate(F'_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → F_1Polygon(O, J'', F_1) → poly3, f_2, o, j''Rotate(M, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → M'Rotate(N, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → N'Segment(M', N') → b'Rotate(L'_5, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → G_1Rotate(L''_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → H_1Segment(G_1, H_1) → pRotate(F'_3, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → I_1Rotate(P, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → P'Segment(I_1, P') → m''Rotate(O, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → O'Rotate(J'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J'''Rotate(F_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J_1Polygon(O', J''', J_1) → poly3', j_2, o', j'''Rotate(M', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → M''Rotate(N', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → N''Segment(M'', N'') → b''Rotate(G_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → Q_1Rotate(H_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → R_1Segment(Q_1, R_1) → p'Rotate(I_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → S_1Rotate(P', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → P''Segment(S_1, P'') → m'''Intersect(d_1, x = 0) → B_2, C_2Line(L, F) → qIntersect(d_1, q) → D_2, E_2CircleSector(L, E_2, B_2) → rRotate(r, If[9 < a < 10, ((-(a - 9)) * π / 4), ((-π)) / 4], L) → r'Segment(L''_2, B) → sSegment(L', A) → tSegment(D, N'') → f_1Segment(H_1, C) → g_1
AI Drawing Prompt Reference
Draw a dynamic 45-45-90 special right triangle in standard position, showing its construction process. Start by creating basic shapes through mirroring and rotation, then use similarity transformations and rotations to generate multiple triangles and polygons, and finally combine them into a complete dynamic template. The process involves angles, trigonometry, and geometric constructions, suitable for high school students.
The prompt above was compiled from the original drawing commands and is for reference only.