相似矩形判定与比例关系互动练习

GeoGebra 命令及参数

1. Random(2, 5) → currScale
2. Random(0, 1) → currType
3. Random(2, floor(33 / (currScale + 1))) → smallWidth
4. If(currType ≟ 0, smallWidth, largeWidth) → ABCDwidth
5. UnicodeToLetter(10003) → cmark
6. Random(1, floor(16 / currScale)) → smallHeight
7. If(currType ≟ 0, smallHeight, largeHeight) → ABCDheight
8. If(currType ≟ 0, largeHeight, smallHeight) → EFGHheight
9. If(currType ≟ 0, largeWidth, smallWidth) → EFGHwidth
10. LaTeX(If[currType ≟ 0, ("\vphantom\dfrac{2}{2}" * currScale), (("\dfrac{1}{" * currScale) * "}")]) → scaleFactorDisp
11. Polygon(E + (1, 1), E + (1, maxDragHeight), E + (maxDragWidth, maxDragHeight), E + (maxDragWidth, 1)) → polyRegion, f, g, h, i
12. LaTeX((("\text{\textbf{Question: }Can you draw a rectangle similar to \(ABCD\) with a scale factor of }" * scaleFactorDisp) * "? ")) → MainInstruc
13. PointIn(polyRegion) → G
14. Intersect(Line[E, yAxis], Line[G, xAxis]) → F
15. Intersect(Line[E, xAxis], Line[G, yAxis]) → H
16. Polygon(E, F, G, H) → studentQuad, e, f_1, g_1, h_1
17. Polygon({E, E + (0, EFGHheight), E + (EFGHwidth, EFGHheight), E + (EFGHwidth, 0)}) → correctQuad
18. Segment(A, B) → ab
19. Segment(B, C) → bc
20. Segment(C, D) → cd
21. Segment(A, D) → ad
22. LaTeX("\text{\textbf{Instructions: }Drag point \(G\) to change the size of rectangle \(EFGH\)}") → SpecInstruc
23. LaTeX((((((((("\text{\textcolor{#1b5e20}{" * correct) * "} The scale factor is \( ") * scaleFactorDisp) * " \), so the new height is \(") * EFGHheight) * " \) and the new width is \(") * EFGHwidth) * " \).}")) → fbCorrect
24. LaTeX((((((((((((((((("\text{\textcolor{#d32f2f}{" * incorrect) * "}Since the scale factor is \(") * scaleFactorDisp) * "\), the new height will be \(") * scaleFactorDisp) * " \times ") * ABCDheight) * " = ") * EFGHheight) * "\), and the new } \\ \text{width will be \(") * scaleFactorDisp) * " \times ") * ABCDwidth) * "=") * EFGHwidth) * "\). Please try again.}")) → fbWrong