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勾股定理与锐角三角形

勾股定理与锐角三角形
几何画板及绘图内容加载中，请稍等……
2018-10-30 09:52
测试改名0三角函数几何作图
①本范例演示勾股定理在锐角三角形中的应用，通过动态演示直角三角形三边关系；②核心数学概念包括勾股定理、锐角三角形性质、动态几何作图；③构造要点运用了UnicodeToLetter, LaTeX, DynamicCoordinates, Polygon, Angle, TableText等GeoGebra命令与对象，实现动态三角形与数据展示；④适合高中数学教学与几何直观理解，可用于探究性学习。

GeoGebra 命令及参数

  1. UnicodeToLetter(10007) → xmark
  2. UnicodeToLetter(10003) → cmark
  3. LaTeX("\text{\textbf{Instructions: }Drag point \(A\) to change the size of \(\angle ACB\). }") → SpecInstruc
  4. DynamicCoordinates(AFree, If[IsInRegion[AFree, cRegion], x(AFree), x(Asave)], If[IsInRegion[AFree, cRegion], y(AFree), y(Asave)]) → A
  5. Polygon(A, C, B) → t1, b, a, c
  6. LaTeX(If[aSqPlusbSq > cSq, "\textbf{\textcolor{red}>}", "="]) → relationship
  7. LaTeX("\text{\textbf{Question: }For a right-angled triangle, the Pythagorean Theorem states \(a^2+ b^2 = c^2\) where \\\(a\) and \(b\) are the legs, and \(c\) is the hypotenuse of the triangle. What happens to this \\relationship if the right angle is made acute?}") → MainInstruc
  8. Angle(B, C, A) → α
  9. TableText({{"", "\textbf{\phantom{ >}}", ""}, {"a^2+b^2", "=", aSqPlusbSq}, {"\phantom{a^2+}c^2", "=", cSq}, {"a^2+b^2", relationship, "c^2"}}) → infoTbl
  10. LaTeX(((MainInstruc * "\\") * SpecInstruc)) → allInstruc