三角形重心与线段交点

三角形重心与线段交点
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2017-11-09 23:35
该范例演示了如何通过几何作图找到三角形的重心,并展示了线段交点的构造方法。核心数学概念包括三角形的重心、线段的交点以及使用GeoGebra命令进行几何构造。通过使用Segment、Point、Intersection等命令,用户可以直观地理解这些概念。适合初中及以上学生学习几何和三角学。

GeoGebra 命令及参数

  1. LaTeX("\text{Simplify each side of the equation.}") → text1_2
  2. LaTeX("\text{Use opposite operations so all variables are on one side of the equation.}") → text1_8
  3. LaTeX("\text{Notice that the variable \textcolor{#000099}{\mathit{x}} is on both sides of the equation.Also notice the set of parentheses in the expression\\on the left side of the equation.}") → text1_1
  4. LaTeX((("\text{Eliminate the parentheses by first distributing the \textcolor{#000099}{2} over \textcolor{#000099}{{" * x1) * "}\mathit{x} + 1}.}")) → text1_4
  5. LaTeX((((((((("\text{\textcolor{#000099}{2({" * x1) * "}\mathit{x} + {") * c1) * "}) = {") * x2) * "}\mathit{x} + {") * c2) * "}}}")) → text1_3
  6. LaTeX("\text{Again,you need to eliminate one of the terms with the variable \textcolor{#000099}{\mathit{x}}.Subtract \textcolor{#000099}{6\mathit{x}} from both expressions of the equation.}") → text1_7
  7. LaTeX((("\text{\textcolor{#000099}{−{" * x2) * "}\mathit{x}}}")) → text2
  8. LaTeX((("\text{\textcolor{#000099}{−{" * x2) * "}\mathit{x}}}")) → text1_9
  9. LaTeX("\text{This equation has no solution.}") → text1_{11}
  10. LaTeX("\text{:}") → text5
  11. LaTeX((("\text{Step {" * Slider) * "} of 12}")) → text7_1
  12. LaTeX("\text{Click the button to solve the problem.}") → text8
  13. LaTeX("\text{\mathbf{Note}\mathbf{:} Use the (Data Kit) \\to return to the original \\problem or randomly generate \\a similar practice problem.\\Use the (Definition) to \\review words to know.}") → text9
  14. LaTeX("\text{\mathbf{Variable:} A characteristic,number,or quantity that increases or decreases\\ over time,or takes different values in different situations. }") → text7
  15. LaTeX((((((((("\text{\textcolor{#000099}{{" * x2) * "}\mathit{x} + {") * sec_1) * "} = {") * x2) * "}\mathit{x} + {") * c2) * "}}}")) → text1_6
  16. LaTeX((((((((("\text{\textcolor{#000099}{{" * x2) * "}\mathit{x} + {") * sec_1) * "} = {") * x2) * "}\mathit{x} + {") * c2) * "}}}")) → text1_{10}
  17. LaTeX((((("\text{Subtracting the variables gives us an impossible result\\\textcolor{#000099}{{" * sec_1) * "} = {") * c2) * "}}.This is not a true statement;therefore,there are no solutions to this equation.}")) → text1_{12}
  18. Segment(A, B) → f
  19. LaTeX((((("\text{RHS Constant:\textcolor{#000099}{{" * x2) * "}\mathit{x}+{") * c2) * "}}}")) → text6_1
  20. LaTeX((((("\text{LHS Co-efficient (\mathit{x}):\textcolor{#000099}{2({" * x1) * "}\mathit{x}+{") * c1) * "})}}")) → text6
  21. LaTeX((((("\text{LHS Constant:\textcolor{#000099}{2({" * x1) * "}\mathit{x}+{") * c1) * "})}}")) → text6_2
  22. LaTeX((((((((("\text{Solve the equation \textcolor{#000099}{2({" * x1) * "}\mathit{x} + {") * c1) * "}) = {") * x2) * "}\mathit{x} + {") * c2) * "}}}.")) → text1
  23. LaTeX((((("\text{Multiply \textcolor{#000099}{2} times \textcolor{#000099}{{" * x1) * "}\mathit{x}} and \textcolor{#000099}{2} times \textcolor{#000099}{{") * c1) * "}}}.")) → text1_5
  24. LaTeX((((("\text\\ \\ \\ \\ \\ \\ \\ \\ \\ {\textcolor{#000099}{{" * sec_1) * "} = ") * c2) * "}}")) → text3