正方形的性质 by David T
几何画板及绘图内容加载中,请稍等……
这个范例演示了正方形的性质,包括对角线相等且互相垂直、边长相等、内角均为90度等。涉及的核心数学概念有几何作图、线段、角度、旋转等。通过使用GeoGebra命令如Circle、Line、OrthogonalLine、Segment、Intersect、Polygon、Midpoint、Rotate等,可以动态展示正方形的性质。适合初中及以上学生学习几何作图和相关性质。
GeoGebra 命令及参数
Circle(A, B) → pLine(A, B) → e_1OrthogonalLine(A, e_1) → iSegment(A, B) → d_1Intersect(p, i) → D, CPolygon(A, D, B) → P, a, b, dMidpoint(D, B) → ERotate(A, (-rotateΔ), E) → A'Rotate(D, (-rotateΔ), E) → D'Rotate(B, (-rotateΔ), E) → B'Polygon(A', D', B') → P', c, e, fOrthogonalLine(B, e_1) → f_3Intersect(f_3, e_1) → FMidpoint(B', A') → GIf(rotateΔ > 0°, G) → KMidpoint(d_1) → MAngle(B', A', D') → γAngle(B, A, D) → δAngle(D, B, A) → ζAngle(D', B', A') → αAngle(A, D, B) → βAngle(A', D', B') → εSegment(D', A') → c_1Segment(A, D) → a_1Segment(B', A') → f_1Segment(A, D) → a_2Segment(D', A') → c_2Segment(B', A') → f_2Segment(A, B) → d_2Segment(D, E) → gSegment(B, E) → g_1Segment(A, E) → hSegment(A', E) → h_1Angle(E, A, D) → ηAngle(B, A, E) → θAngle(D, A', E) → ιAngle(E, A', B) → κAngle(A, D, A') → λAngle(A', B, A) → μLine(E, e_1) → jLine(E, f_3) → kPoint(j) → LPoint(j) → NPoint(k) → OPoint(k) → QSegment(O, Q) → lSegment(L, N) → mIntersect(p, i, 2) → ILine(A, E) → qPoint(q) → HPoint(q) → JSegment(H, J) → sPolygon(A, D, A', B) → P'', a_3, d_3, a', b_1Rotate(A, turn, E) → A'_1Rotate(D, turn, E) → D'_1Rotate(A', turn, E) → A''Rotate(B, turn, E) → B'_1Rotate(A, (-turn), E) → A'_2Rotate(D, (-turn), E) → D'_2Rotate(A', (-turn), E) → A''_1Rotate(B, (-turn), E) → B'_2Polygon(A'_2, D'_2, A''_1, B'_2) → P''', a'_2, d'_2, a''_1, b'_2Angle(D, E, A) → νLine(E, D) → nPoint(n) → RPoint(n) → SSegment(R, S) → rPolygon(A, D, A', B) → polyfold, a_4, d_4, a'_1, b_2LineBisector(drag, A') → tIntersect(t, f) → UIntersect(c, a'_1) → VIntersect(t, c) → WPolygon(U, drag, W) → poly1, w, u, t_1Intersect(t, a) → ZOrthogonalLine(drag, u) → i_1Line(Z, u) → j_1Intersect(i_1, j_1) → A_1Polygon(W, drag, A_1, Z) → poly2, w_1, t_2, a_5, zOrthogonalLine(drag, w) → k_1Intersect(t, d) → B_1Line(B_1, w) → l_1Intersect(k_1, l_1) → C_1Polygon(U, drag, C_1, B_1) → poly3, u_1, t_3, c_3, b_3LineBisector(peel, B) → m_1Intersect(m_1, c) → D_1Intersect(m_1, d) → E_1Polygon(peel, E_1, D_1) → poly4, d_5, t_4, e_2Intersect(f, d_4) → F_1Intersect(m_1, f) → G_1OrthogonalLine(peel, d_5) → n_1Line(G_1, d_5) → p_1Intersect(n_1, p_1) → H_1Polygon(peel, E_1, G_1, H_1) → poly5, t_5, e_3, g_2, h_2Intersect(m_1, a) → I_1OrthogonalLine(peel, e_2) → q_1Line(I_1, e_2) → r_1Intersect(r_1, q_1) → J_1Polygon(peel, D_1, I_1, J_1) → poly6, t_6, d_6, i_2, j_2
AI 绘图提示语参考
绘制一个正方形,包括其对角线、边和角度。首先画一个圆和一条线,然后构造正方形的两条对角线,接着画正方形的边并旋转正方形,最后标注所有角度并确保对角线相等且垂直。
以上提示语为根据原始绘图命令整理而来,仅供参考。