直角三角形构造示例

GeoGebra 命令及参数

1. LaTeX("\text{Set up an equation by using the Pythagorean Theorem.}") → text1
2. LaTeX("\text{Because the piece of tile is a triangle with two perpendicular sides, it is in the shape of a right triangle. This means that }") → text2
3. LaTeX("\text{is the length of the hypotenuse, can be used to find the length of the remaining side.}") → text4
4. LaTeX("\text{Determine the length of the remaining side.}") → text6
5. LaTeX("\text{Equation from the previous step}") → text9
6. LaTeX("\text{Take the positive square root of both sides of}") → text15
7. LaTeX("\text{the equation using a calculator.}") → text16
8. LaTeX("\text{Simplify the square root.}") → text18
9. Segment(B, (x(B), 0)) → b
10. Segment((0, 2), A) → a
11. Point(a) → Q
12. Vector(Q, B) → u
13. Sequence(Segment[A + (a, 0), A + (a, (-0.6))], a, 0, 10) → list1
14. Sequence(Segment[A + (a - 0.5, 0), A + (a - 0.5, (-0.4))], a, 1, 10) → list2
15. Segment((0, 0), C) → c
16. Vector(D, E) → v
17. Segment(E, (x(E), 0)) → d
18. LaTeX((((("\text{Using the Pythagorean Theorem, the equation is \textcolor{#000099}{" * value1) * "^{2}+") * value2) * "^{2}=c^{2}}.}")) → text5
19. LaTeX((("\text{A side length cannot be negative, so consider only the positive square root value of \textcolor{#000099}{" * total) * "}. Therefore, the length of the}")) → text19
20. LaTeX((((("\text{To determine the length of the remaining side, solve the equation \textcolor{#000099}{" * value1) * "^{2}+") * value2) * "^{2}=c^{2}} for \textcolor{#000099}{c}.}")) → text7
21. LaTeX("\text{{the Pythagorean Theorem, which is \textcolor{#000099}{a^{2}+b^{2}=c^{2}}, where \textcolor{#000099}{a} and \textcolor{#000099}{b} are the lengths of the legs of a right triangle and \textcolor{#000099}{c}}") → text3
22. LaTeX("\text{ \mathbf{Congruent} figures are congruent if they have the same shape, size, lines, and }") → text34
23. LaTeX((((("\text{\textcolor{#000099}{" * value1) * "^{2}+") * value2) * "^{2}}}")) → text8
24. LaTeX((((("\text{\textcolor{#000099}{" * squareval1) * "+") * squareval2) * "}}")) → text10
25. LaTeX((("\text{\textcolor{#000099}{" * total) * "}}")) → text12
26. LaTeX("\text{\textcolor{#000099}{=\;c^{2}}}") → text38
27. LaTeX("\text{\textcolor{#000099}{=\;c^{2}}}") → text37
28. LaTeX("\text{\textcolor{#000099}{=\;c^{2}}}") → text39
29. LaTeX("\text{\textcolor{#000099}{\;=\sqrt{c^{2}}}") → text41
30. LaTeX((("\text{\textcolor{#000099}{" * result) * "}}")) → text17
31. LaTeX("\text{\textcolor{#000099}{=\;c}") → text42
32. LaTeX("\text{\mathbf{Congruent \;triangles} triangles having the same angle measures and side lengths.}") → text36
33. LaTeX("\text{angles; the symbol for representing congruency between figures is ≅.}") → text35
34. LaTeX((("\text{\textcolor{#000099}{\sqrt{" * total) * "}}}")) → text14
35. LaTeX("\text{The two perpendicular sides form a right angle, so they are the legs of the triangle. The hypotenuse is the side opposite}") → newt43
36. LaTeX((((("\text{the right angle. Therefore, given \textcolor{#000099}{a^{2}+b^{2}=c^{2},} the variables \textcolor{#000099}{a} and \textcolor{#000099}{b} represent the leg lengths (\textcolor{#000099}{" * value1) * "} cm and \textcolor{#000099}{") * value2) * "} cm),}")) → newt43_1
37. LaTeX("\text{and \textcolor{#000099}{c} represents the hypotenuse.}") → newt43_2
38. LaTeX("\text{A carpenter cuts a piece of tile into a triangle. Two of the sides are perpendicular. The two perpendicular sides}") → Question1
39. LaTeX((((("\text{measure \textcolor{#000099}{" * value1) * "} centimeters and \textcolor{#000099}{") * value2) * "} centimeters. What is the length of the remaining side of the piece of tile?}")) → Question2
40. LaTeX((((("\text{Square \textcolor{#000099}{" * value1) * "} and \textcolor{#000099}{") * value2) * "}.}")) → text11
41. LaTeX("\text{Add.}") → text13
42. LaTeX((("\text{remaining side of the piece of tile is \textcolor{#000099}{ " * result) * "} centimeters.}")) → text20