正方體的切面 Sections of the Cube
根據老師指示，構作以下的圖形。
Construct the following figures according to the teacher's instruction.
課業 Task
利用已構作的立體圖形，探究正方體有甚麼形狀的截面。
Investigate the possible shapes of the sections of a cube with the figures you constructed.
(a) 正方體能否有不等邊三角形的截面？如有，將有不等邊三角形截面的圖形以"3_yourname(scalene).ggb" 的檔案名稱儲存，其中 yourname 是你的英文名字，然後連本節同其他課業的答案以標題 "Lesson 3 Assignment" 電郵至 geogebra.hk@gmail.com。
Can the cube have a section in the shape of a scalene triangle? If yes, save your figure with a scalene triangle section in the file name "3_yourname(scalene).ggb", where yournameis your name in English.
(b) 正方體能否有等腰三角形的截面？如有，將有等腰三角形截面的圖形以"3_yourname(isosceles).ggb" 的檔案名稱儲存，然後連本節同其他課業的答案以標題 "Lesson 3 Assignment" 電郵至 geogebra.hk@gmail.com。
Can the cube have a section in the shape of an isosceles triangle? If yes, save your figure with an isosceles triangle section in the file name "3_yourname(isosceles).ggb".(c) 正方體能否有等邊三角形的截面？如有，將有等邊三角形截面的圖形以"3_yourname(isosceles).ggb" 的檔案名稱儲存，然後連本節同其他課業的答案以標題 "Lesson 3 Assignment" 電郵至 geogebra.hk@gmail.com。
Can the cube have a section in the shape of an equilateral triangle? If yes, save your figure with an equilateral triangle section in the file name "3_yourname(equilateral).ggb".
(d) 正方體能否有長方形、菱形、平行四邊形或梯形的截面？如有，將有相關形狀截面的圖形以"3_yourname(shape).ggb" 的檔案名稱儲存，其中 shape 是 "rectangle", "rhombus", "parallelogram" 或 "trapezium"，然後連本節同其他課業的答案以標題 "Lesson 3 Assignment" 電郵至 geogebra.hk@gmail.com。
Can the cube have a section in the shape of a rectangle, a rhombus, a parallelogram or a trapezium? If yes, save your figure with the shape in the file name "3.2_yourname(shape).ggb" where "shape" is either "rectangle", "rhombus", "parallelogram" or "trapezium".(e) 正方體能否有五邊形或六邊形的截面？如有，將有相關形狀截面的圖形以"3_yourname(shape).ggb" 的檔案名稱儲存，其中 shape 是 "pentagon" 或 "hexagon"，然後連本節同其他課業的答案以標題 "Lesson 3 Assignment" 電郵至 geogebra.hk@gmail.com。
Can the cube have a section in the shape of a pentagon (五邊形) a hexagon (六邊形)? If yes, save your figure with the shape in the file name "3.2_yourname(shape).ggb" where "shape" is either "pentagon" or "hexagon".