NTM3A_supp_C04立體圖形的探究

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第 4 章 立體圖形的探究 4.1 第 4 章 立體圖形的探究 【本章各練習均中英對照，以供參考。】 熱身練習 1. 寫出下列各立體的名稱。 1. Write down the name of each of the following solids. (a) (b) (c) 2. 把下列各柱體的均勻橫切面填上顏色。 【附錄已提供下列各圖的複本。】 2. Colour the uniform cross-section of each of the following prisms. [ Copy of each figure is provided in the Appendix. ] (a) (b) (c) 3. 繪畫下列各圖形的所有對稱軸，並指出 圖形屬何種軸對稱。 【附錄已提供下列各圖的複本。】 3. Draw all axes of symmetry of the following figures and state the type of reflectional symmetry for each figure. [ Copy of each figure is provided in the Appendix. ] (a) (b) (c) 4. 下列各圖形屬多少重旋轉對稱？由此， 標出它們的旋轉中心。 【附錄已提供下列各圖的複本。】 4. How many folds of rotational symmetry does each of the following figures have? Hence mark the centre of rotation in each figure. [ Copy of each figure is provided in the Appendix. ]
練習 4A 初級 組合 4.2 數學新里程 中三上 — 初中附加練習 (a) (b) (c) 5. 分別在等距方格和斜網格上繪畫下列各 立體。 ( 圖中的數字表示立體的邊長。 ) 【附錄已提供等距方格和斜網格。】 5. Draw each of the following solids on isometric grid and oblique grid. (The numbers in the figures show the lengths of the corresponding sides of the solids.) [ Copy of each of the isometric grid and oblique grid is provided in the Appendix. ] (a) 2 4 6 (b) 2 2 2 2 10 4 4 6 4 2 (c) 2 6 8 8 4 4 2 2 強化練習 【本部分為書中每個練習額外提供兩種不同的題目組合：「初級組合」和「高級組合」。同學可按其需要選擇完 成 其中一組 題目。】 練習 4A  初 級 組 合 程度一 1. 繪畫下列各立體圖形其中 1 個反射面。 【附錄已提供下列各圖的複本。】 1. For each of the following solids, draw one of its planes of reflection. [ Copy of each solid is provided in the Appendix. ] (a) 直立三角柱體 (b) 直立半圓柱體 (c) 直立正六角柱體 [ Right triangular prism ] [ Half of right cylinder ] [ Right regular hexagonal prism ] 練習 4A 初級 組合
第 4 章 立體圖形的探究 4.3 2. 繪畫下列各立體圖形其中 1 條旋轉軸。 【附錄已提供下列各圖的複本。】 2. For each of the following solids, draw one of its axes of rotation. [ Copy of each solid is provided in the Appendix. ] (a) 直立角柱體 (b) 直立角柱體 (c) 直立長方錐體 [ Right prism ] [ Right prism ] [ Right rectangular pyramid ] 3. 下列各物件有多少個反射面？ 3. How many planes of reflection does each of the following objects have? (a) (b) (c) 4. 下列各物件有多少條旋轉軸？ 4. How many axes of rotation does each of the following objects have? (a) (b) (c) 5. 下圖所示為一個立體的一半，其中陰影 部分為立體的反射面。試繪畫立體的另 一半。 【附錄已提供下圖的複本。】 5. The figure shows half of a solid, where the shaded region is the plane of reflection. Draw another half of the solid. [ Copy of the figure is provided in the Appendix. ] 練習 4A 初級 組合
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練習 4A 初級 組合 4.4 數學新里程 中三上 — 初中附加練習 6. 若把下列各摺紙圖樣沿虛線摺成一個立 體，問該立體的名稱是甚麼？ 6. If each of the following nets is folded up along the dotted lines to form a hollow solid, what kind of solid will you get? (a) (b) (c) 7. 若把下列各立體沿灰色邊剪開，試繪畫 各立體拆開後的摺紙圖樣。 7. If each of the following hollow solids is cut along the grey edges, draw its net. (a) 直立三角柱體 (b) 直立長方錐體 (c) 長方體 [ Right triangular prism ] [ Right rectangular [ Cuboid ] pyramid ] 8. 試繪畫一種可以摺成下列各立體的摺紙 圖樣。 8. Draw a net for each of the following hollow solids. (a) 正四面體 (b) 直立三角柱體 (c) 直立角柱體 [ Regular tetrahedron ] [ Right triangular prism ] [ Right prism ] 程度二
第 4 章 立體圖形的探究 4.5 9. 在下列各立體圖形中繪畫所有反射面， 由此求各立體的反射面數目。 【附錄已提供下列各圖的複本。】 9. Draw the planes of reflection of each of the following solids, and hence find the number of planes of reflection of each solid. [ Copy of each solid is provided in the Appendix. ] (a) 直立長方錐體 (b) 直立角柱體 (c) 直立圓柱體 正方體 [ Right rectangular [ Right prism ] [ Right cylinder cube ] pyramid ] 10. 在下列各立體圖形中繪畫所有旋轉軸， 由此求各立體的旋轉軸數目。對於每條 旋轉軸，該立體具有多少重旋轉對稱的 性質？ 【附錄已提供下列各圖的複本。】 10. Draw the axes of rotation of each of the following solids, and hence find the number of axes of rotation of each solid. For each axis of rotation, how many folds of rotational symmetry are there? [ Copy of each solid is provided in the Appendix. ] (a) 直立正方錐體 (b) 直立角柱體 (c) 直立正六角柱體 [ Right square-based [ Right prism ] [ Right regular pyramid ] hexagonal prism ] 11. 下圖所示為一立體的摺紙圖樣。 11. The figure shows the net of a hollow solid. 練習 4A 初級 組合
練習 4A 初級 組合 練習 4A 高級 組合 4.6 數學新里程 中三上 — 初中附加練習 D B C H A F E G (a) 這個立體的名稱是甚麼？ (b) 把該摺紙圖樣摺成立體後， D 點會與 哪一點重疊？ (c) 把該摺紙圖樣摺成立體後， E 點會與 哪一點重疊？ (a) What kind of solid is it? (b) When the net is folded up to form a solid, which point will coincide with point D ? (c) When the net is folded up to form a solid, which point will coincide with point E ? 12. 下圖所示為一立體的摺紙圖樣，其中所 有角均為直角。 12. The figure shows the net of a hollow solid where all the angles there are right angles. (a) 繪畫該立體的平面圖像。 (b) 該立體共有多少個反射面？ (c) 該立體共有多少條旋轉軸？對於每 條所得旋轉軸，該立體具有多少重 旋轉對稱的性質？ (a) Draw the plane figure of the solid. (b) How many planes of reflection are there in this solid? (c) How many axes of rotation are there in this solid? How many folds of rotational symmetry are there for each axis of rotation?  高 級 組 合 程度一 1. 繪畫下列各立體圖形其中 2 個反射面和 1 條旋轉軸。 【附錄已提供下列各圖的複本。】 1. For each of the following solids, draw two of its planes of reflection and one of its axes of rotation. [ Copy of each solid is provided in the Appendix. ] (a) 直立角柱體 (b) 半球體 直立圓柱體 (c) 直立角柱體 [ Right prism ] [ Hemisphere [ Right prism ] right cylinder ]
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第 4 章 立體圖形的探究 4.7 2. 下列各物件有多少個反射面？ 2. How many planes of reflection does each of the following objects have? (a) (b) (c) 3. 下列各物件有多少條旋轉軸？ 3. How many axes of rotation does each of the following objects have? (a) (b) (c) 4. 若把下列各摺紙圖樣沿虛線摺成一個立 體，問該立體的名稱是甚麼？ 4. If each of the following nets is folded up along the dotted lines to form a hollow solid, what kind of solid will you get? (a) (b) (c) 5. 若把下列各立體沿灰色邊剪開，試繪畫 立體拆開後的摺紙圖樣。 5. If each of the following hollow solids is cut along the grey edges, draw its net. (a) 長方體 (b) 直立正五角錐體 (c) 直立正六角柱體 [ Cuboid ] [ Right regular [ Right regular pentagonal pyramid ] hexagonal prism ] 練習 4A 高級 組合
練習 4A 高級 組合 4.8 數學新里程 中三上 — 初中附加練習 6. 試繪畫兩種可以摺成下列各立體的摺紙 圖樣。 6. Draw 2 different nets for each of the following hollow solids. (a) 直立半圓柱體 (b) 直立正六角錐體 (c) 直立正十角柱體 [ Half of right cylinder ] [ Right regular [ Right regular hexagonal pyramid ] decagonal prism ] 程度二 7. 在下列各立體圖形中繪畫所有反射面， 由此求各立體的反射面數目。 【附錄已提供下列各圖的複本。】 7. Draw the planes of reflection of each of the following solids, and hence find the number of planes of reflection of each solid. [ Copy of each solid is provided in the Appendix. ] (a) 直立角柱體 (b) 長方體 直立圓柱體 (c) 直立正八角柱體 [ Right prism ] [ Cuboid right cylinder ] [ Right regular octagonal prism ] 8. 在下列各立體圖形中繪畫所有旋轉軸， 由此求各立體的旋轉軸數目。對於每條 旋轉軸，該立體具有多少重旋轉對稱的 性質？ 【附錄已提供下列各圖的複本。】 8. Draw the axes of rotation of each of the following solids, and hence find the number of axes of rotation of each solid. For each axis of rotation, how many rotational symmetry are there? [ Copy of each solid is provided in the Appendix. ] (a) 直立圓錐體 (b) 兩個直立正方錐體 (c) 直立正十角柱體 [ Right cone ] 長方體 [ Right regular [ Two right square-based decagonal prism ] pyramids cuboid ]
第 4 章 立體圖形的探究 4.9 9. 下圖所示為一直立角柱體。 9. The figure shows a right prism. (a) 求該立體的反射面數目。 (b) 求該立體的旋轉軸數目。對於每條旋 轉軸，該立體具有多少重旋轉對稱 的性質？ (c) 試繪畫一個可以摺成該立體的摺紙 圖樣。 (a) Find the number of planes of reflection of the prism. (b) Find the number of axes of rotation of the prism. Hence find the number of folds of rotational symmetry for each axis of rotation. (c) Draw a net of the prism. 10. 下圖所示為一立體的摺紙圖樣。 10. The figure shows the net of a hollow solid. C B A H G F D E (a) 繪畫該立體的平面圖像。 (b) 把該摺紙圖樣摺成立體後， H 點會 與哪一點重疊？ (c) 把該摺紙圖樣摺成立體後， G 點會 與哪一點重疊？ (a) Draw the plane figure of the solid. (b) When the net is folded up to form a solid, which point will coincide with point H ? (c) When the net is folded up to form a solid, which point will coincide with point G ? 11. 下圖所示為一立體的摺紙圖樣，其中所 有角均為直角。 11. The figure shows the net of a hollow solid where all the angles there are right angles. 練習 4A 高級 組合
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練習 4A 高級 組合 練習 4B 初級 組合 4.10 數學新里程 中三上 — 初中附加練習 (a) 繪畫該立體的平面圖像。 (b) 該立體共有多少個反射面？ (c) 該立體共有多少條旋轉軸？對於每 條所得旋轉軸，該立體具有多少重 旋轉對稱的性質？ (a) Draw the plane figure of the solid. (b) How many planes of reflection are there in this solid? (c) How many axes of rotation are there in this solid? How many folds of rotational symmetry are there for each axis of rotation? 12. 已知一粒骰子任何一面的點數與其對應 背面的點數之和均為 7 。下列各圖為未完 成 的骰 子 摺 紙圖 樣， 試 完成該 摺紙 圖 樣。 【附錄已提供下列各圖的複本。】 12. It is known that the sum of the dots on any face of a dice and its opposite face is 7. The figures below show the nets of incomplete dice. Complete the nets. [ Copy of each figure is provided in the Appendix. ] (a) (b) (c) 練習 4B 【附錄已提供方格紙、等距方格和斜網格。】  初 級 組 合 程度一 1. 繪畫下列各立體的正投影圖。 1. Draw the orthographic projection of each of the following solids. (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 2. 繪畫下列各立體的正投影圖。 2. Draw the orthographic projection of each of the following solids.
第 4 章 立體圖形的探究 4.11 (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 3. 根據下列正投影圖的資料，繪畫均角投 影圖。 3. Draw the isometric projection of each of the following solids according to its orthographic projection. (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view 4. 根據下列正投影圖的資料，繪畫斜角投 影圖。 4. Draw the oblique projection of each of the following solids according to its orthographic projection. (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view 程度二 5. 繪畫下列各立體的正投影圖。 5. Draw the orthographic projection of each of the following solids. 練習 4B 初級 組合
練習 4B 初級 組合 4.12 數學新里程 中三上 — 初中附加練習 (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 6. 繪畫下列各立體的正投影圖。 6. Draw the orthographic projection of each of the following solids. (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 7. 根據下列正投影圖的資料，繪畫均角投 影圖。 7. Draw the isometric projection of each of the following solids according to its orthographic projection. (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view 8. 根據下列正投影圖的資料，繪畫斜角投 影圖。 8. Draw the oblique projection of each of the following solids according to its orthographic projection.
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第 4 章 立體圖形的探究 4.13 (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view  高 級 組 合 程度一 1. 繪畫下列各立體的正投影圖。 1. Draw the orthographic projection of each of the following solids. (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 2. 繪畫下列各立體的正投影圖。 2. Draw the orthographic projection of each of the following solids. (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 3. 根據下列正投影圖的資料，繪畫均角投 影圖。 3. Draw the isometric projection of each of the following solids according to its orthographic projection. 練習 4B 高級 組合
練習 4B 高級 組合 4.14 數學新里程 中三上 — 初中附加練習 (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view 4. 根據下列正投影圖的資料，繪畫斜角投 影圖。 4. Draw the oblique projection of each of the following solids according to its orthographic projection. (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view 程度二 5. 繪畫下列各立體的正投影圖。 5. Draw the orthographic projection of each of the following solids. (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 6. 繪畫下列各立體的正投影圖。 6. Draw the orthographic projection of each of the following solids.
第 4 章 立體圖形的探究 4.15 (a) 俯視 Top view 側視 Side view 正視 Front view (b) 俯視 Top view 側視 Side view 正視 Front view (c) 俯視 Top view 側視 Side view 正視 Front view 7. 根據下列正投影圖的資料，繪畫均角投 影圖。 7. Draw the isometric projection of each of the following solids according to its orthographic projection. (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view 8. 根據下列正投影圖的資料，繪畫斜角投 影圖。 8. Draw the oblique projection of each of the following solids according to its orthographic projection. (a) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (b) 俯視圖 Top view 側視圖 Side view 正視圖 Front view (c) 俯視圖 Top view 側視圖 Side view 正視圖 Front view 練習 4C  初 級 組 合 程度一 1. 下圖所示為一直立三角柱體。試標出所 有連接各頂點而成的直角。 【附錄已提供下圖的複本。】 1. The figure shows a right triangular prism. Mark all right angles at the vertice. [ Copy of the figure is provided in the Appendix. ] 練習 4B 高級 組合 練習 4C 初級 組合
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練習 4C 初級 組合 4.16 數學新里程 中三上 — 初中附加練習 T S U R Q P 2. 下圖中， ABCDEFGH 為一長方體。試繪 畫 線 段 AH 和 其 在 平 面 EFGH 上 的 投 影，並標出它們之間的夾角。 【附錄已提供下圖的複本。】 2. In the figure, ABCDEFGH is a cuboid. Draw the line segment AH and its projection on the plane EFGH , and mark the angle between them. [ Copy of the figure is provided in the Appendix. ] A F E H C B G D 3. 下圖中， VABCD 為一直立長方錐體。試 繪畫線段 VA 在平面 ABCD 上的投影， 並標出它們之間的夾角。 【附錄已提供下圖的複本。】 3. In the figure, VABCD is a right rectangular pyramid. Draw the projection of the line segment VA on the plane ABCD , and mark the angle between them. [ Copy of the figure is provided in the Appendix. ] A B C V D 4. 下圖所示為一直立正六角柱體。試標出 線段 IB 與平面 ABCDEF 的相交角。 【附錄已提供下圖的複本。】 4. The figure shows a right regular hexagonal prism. Mark the angle between the line segment IB and the plane ABCDEF . [ Copy of the figure is provided in the Appendix. ]
第 4 章 立體圖形的探究 4.17 C B A D E F I J G L H K 5. 下圖中， VABCDEF 為一直立正六角錐 體。試標出線段 VE 與底 ABCDEF 的相 交角。 【附錄已提供下圖的複本。】 5. In the figure, VABCDEF is a right regular hexagonal pyramid. Mark the angle between the line segment VE and the base ABCDEF . [ Copy of the figure is provided in the Appendix. ] F E D A V B C 6. 下圖中， ABCD 為一正四面體。 E 是 A 在 平面 BCD 上的投影。試標出線段 AC 與 平面 BCD 的相交角。 【附錄已提供下圖的複本。】 6. In the figure, ABCD is a regular tetrahedron. E is the projection of A on the plane BCD . Mark the angle between the line segment AC and the plane BCD . [ Copy of the figure is provided in the Appendix. ] D A B C E 程度二 7. 下圖所示為一正方體。試標出平面 ABFE 與平面 EFGH 的相交角。 【附錄已提供下圖的複本。】 7. The figure shows a cube. Mark the angle between the planes ABFE and EFGH . [ Copy of the figure is provided in the Appendix. ] 練習 4C 初級 組合
練習 4C 初級 組合 練習 4C 高級 組合 4.18 數學新里程 中三上 — 初中附加練習 G B A F E D H C 8. 下圖中， ABCDEFGH 為一直立角柱體。 P 是 AB 上的一點。試標出平面 PEH 與平 面 EFGH 的相交角。 【附錄已提供下圖的複本。】 8. In the figure, ABCDEFGH is a right prism. P is a point on AB . Mark the angle between the planes PEH and EFGH . [ Copy of the figure is provided in the Appendix. ] D C B P A G H E F 9. 下圖中， ABCDEFGH 為一正方體。試標 出平面 BFH 與平面 EFGH 的相交角。 【附錄已提供下圖的複本。】 9. In the figure, ABCDEFGH is a cube. Mark the angle between the planes BFH and EFGH . [ Copy of the figure is provided in the Appendix. ] C H E B A F D G  高 級 組 合 程度一 1. 下圖所示為一正方錐體。已知 VA 是該錐 體的高，試標出所有連接各頂點而成的 直角。 【附錄已提供下圖的複本。】 1. The figure shows a square-based pyramid. It is known that VA is the height of the pyramid. Mark all right angles at the vertice. [ Copy of the figure is provided in the Appendix. ]
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第 4 章 立體圖形的探究 4.19 C B A V D 2. 下圖中， VABCD 為一直立長方錐體， M 為 AB 的中點。試繪畫線段 VM 和其在平 面 ABCD 上的投影，並標出它們之間的 夾角。 【附錄已提供下圖的複本。】 2. In the figure, VABCD is a right rectangular pyramid, M is the mid-point of AB . Draw the line segment VM and its projection on the plane ABCD , and mark the angle between them. [ Copy of the figure is provided in the Appendix. ] A B C V D M 3. 下圖所示為一直立正五角柱體。試標出 線段 CF 與平面 FGHIJ 的相交角。 【附錄已提供下圖的複本。】 3. The figure shows a right regular pentagonal prism. Mark the angle between the line segment CF and the plane FGHIJ . [ Copy of the figure is provided in the Appendix. ] C I J F G A E D H B 4. 下圖中， VABC 為一三角錐體。試標出線 段 VC 與平面 ABC 的相交角。 【附錄已提供下圖的複本。】 4. In the figure, VABC is a triangular pyramid. Mark the angle between the line segment VC and the plane ABC . [ Copy of the figure is provided in the Appendix. ] 練習 4C 高級 組合
練習 4C 高級 組合 4.20 數學新里程 中三上 — 初中附加練習 C B A V 程度二 5. 下圖所示為一直立三角柱體。試標出平 面 ABFE 與平面 ABCD 的相交角。 【附錄已提供下圖的複本。】 5. The figure shows a right triangular prism. Mark the angle between the planes ABFE and ABCD . [ Copy of the figure is provided in the Appendix. ] B A E F C D 6. 下圖所示為一長方體。試標出平面 ABE 與平面 ABGH 的相交角。 【附錄已提供下圖的複本。】 6. The figure shows a cuboid. Mark the angle between the planes ABE and ABGH . [ Copy of the figure is provided in the Appendix. ] C E D A B G F H 7. 下 圖所 示 為 一角 錐體 ， 它的底 為四 邊 形。試標出平面 VCD 與平面 ABCD 的相 交角。 【附錄已提供下圖的複本。】 7. The figure shows a pyramid with a quadrilateral base. Mark the angle between the planes VCD and ABCD . [ Copy of the figure is provided in the Appendix. ]
第 4 章 立體圖形的探究 4.21 C D B V A 8. 下圖所示為一直立三角柱體。試標出平 面 ADE 與平面 ABC 的相交角。 【附錄已提供下圖的複本。】 8. The figure shows a right triangular prism. Mark the angle between the planes ADE and ABC . [ Copy of the figure is provided in the Appendix. ] F A B E D C 9. 下圖所示為一正八面體。 9. The figure shows a regular octahedron. D A B F E C (a) 試標出線段 AE 與平面 BCDE 的相交 角。 (b) 試標出平面 ABC 與平面 BCDE 的相 交角。 (c) 試標出平面 ADE 與平面 DEF 的相交 角。 (d) 試標出線段 AB 與平面 ACFE 的相交 角。 【附錄已提供上圖的複本。】 (a) Mark the angle between the line segment AE and the plane BCDE . (b) Mark the angle between the planes ABC and BCDE . (c) Mark the angle between the planes ADE and DEF . (d) Mark the angle between the line segment AB and the plane ACFE . [ Copy of the figure is provided in the Appendix. ] 練習 4C 高級 組合
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4.22 數學新里程 中三上 — 初中附加練習 本章測驗 ( 時限： 1 小時 ) 【附錄已提供方格紙、等距方格和斜網格。】 甲部 (1) [ 每題 3 分 ] 1. 求下圖中角柱體的反射面和旋轉軸的數 目。 1. Find the number of planes of reflection and axes of rotation for the following prism. 2. 下圖所示為一立體的摺紙圖樣。 2. The figure shows the net of a hollow solid. (a) 該立體的名稱是甚麼？ (b) 該立體共有多少條旋轉軸？ (a) What kind of solid is it? (b) How many axes of rotation are there in this solid? 3. 試 繪畫 一 種 可摺 成以 下 立體的 摺紙 圖 樣。 3. Draw a net of the following hollow solid. 直立長方錐體 [ Right rectangular pyramid ] 4. 若把下圖中的立體沿灰色邊剪開，試繪 畫立體拆開後的摺紙圖樣。 4. If the following hollow solid is cut along the grey edges, draw its net.
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第 4 章 立體圖形的探究 4.23 正方體 [ Cube ] 5. 下圖中， ABCDEFGH 是一直立角柱體。 試標出平面 ABHE 與平面 EFGH 的相交 角。 【附錄已提供下圖的複本。】 5. In the figure, ABCDEFGH is a right prism. Mark the angle between the planes ABHE and EFGH . [ Copy of the figure is provided in the Appendix. ] D C B A G H E F 6. 下 圖 中 ， VABCDE 為 一 直 立 正 五 角 錐 體。試標出線段 VA 與平面 ABCDE 的相 交角。 【附錄已提供下圖的複本。】 6. In the figure, VABCDE is a right regular pentagonal pyramid. Mark the angle between the line segment VA and the plane ABCDE . [ Copy of the figure is provided in the Appendix. ] V D A B C E 甲部 (2) [ 每題 6 分 ] 7. 繪畫以下立體的正投影圖。 7. Draw the orthographic projection of the following solid.
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4.24 數學新里程 中三上 — 初中附加練習 俯視 Top view 側視 Side view 正視 Front view 8. 繪畫以下立體的正投影圖。 8. Draw the orthographic projection of the following solid. 俯視 Top view 側視 Side view 正視 Front view 9. 根據以下正投影圖的資料，繪畫均角投 影圖。 9. Draw the isometric projection of the solid according to its orthographic projection. 俯視圖 Top view 側視圖 Side view 正視圖 Front view 10. 根據以下正投影圖的資料，繪畫斜角投 影圖。 10. Draw the oblique projection of the solid according to its orthographic projection.
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第 4 章 立體圖形的探究 4.25 俯視圖 Top view 側視圖 Side view 正視圖 Front view 乙部 11. 以下為一立體的正投影圖。 11. The following is the orthographic projection of a solid. 俯視圖 Top view 側視圖 Side view 正視圖 Front view (a) 繪畫該立體的均角投影圖。 (5 分 ) (b) 該立體共有多少個反射面？ (2 分 ) (c) 該立體共有多少條旋轉軸？ (2 分 ) (d) 繪畫一種可摺成該立體的摺紙圖樣。 (4 分 ) (a) Draw the isometric projection of the solid. (5 marks) (b) How many planes of reflection are there in this solid? (2 marks) (c) How many axes of rotation are there in this solid? (2 marks) (d) Draw a net of the solid. (4 marks) 多項選擇題 [ 每題 3 分 ] 12. 下列哪一條不可能是圖中正方體的旋轉 軸？ 12. Which of the following cannot be the axis of rotation of the cube?
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4.26 數學新里程 中三上 — 初中附加練習 L 3 L 1 L 4 L 2 A. L 1 B. L 2 C. L 3 D. L 4 □ A. L 1 B. L 2 C. L 3 D. L 4 □ 13. 下圖中的角柱體共有多少個反射面？ 13. How many planes of reflection does the following prism have? A. 2 B. 3 C. 4 D. 5 □ A. 2 B. 3 C. 4 D. 5 □ 14. 下圖所示為一直立正五角柱體。問該立 體共有多少條旋轉軸？ 14. The figure shows a right regular pentagonal prism. How many axes of rotation does the prism have?
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第 4 章 立體圖形的探究 4.27 A. 1 B. 2 C. 5 D. 6 □ A. 1 B. 2 C. 5 D. 6 □ 15. 下列哪一個立體只具有二重旋轉對稱的 性質？ 15. Which of the following has only 2-fold rotational symmetry? A. 正方體 Cube B. 球體 Sphere C. 長方體 Cuboid D. 正三角柱體 Regular triangular prism □ 16. 下圖所示為一正方體的摺紙圖樣。把該 摺紙圖樣摺成立體後， I 點會與哪一點重 疊？ 16. The figure shows the net of a hollow cube. When the net is folded up to form the cube, which point will coincide with point I ?
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4.28 數學新里程 中三上 — 初中附加練習 E D C H I J K F G L N M B A A. M B. N C. L D. G □ A. M B. N C. L D. G □ 17. 下列哪一個不是正方體的摺紙圖樣？ 17. Which of the following is not a net of a cube? A. B. C. D. □ 18. 下列哪一幅是以下立體的俯視圖？ 18. Which of the following is the top view of the solid below?
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第 4 章 立體圖形的探究 4.29 俯視 Top view 側視 Side view 正視 Front view A. B. C. D. □ 19. 下列哪一幅是以下立體的正視圖？ 19. Which of the following is the front view of the solid below?
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4.30 數學新里程 中三上 — 初中附加練習 俯視 Top view 側視 Side view 正視 Front view A. B. C. D. □ 20. 下列哪一幅是以下立體的側視圖？ 20. Which of the following is the side view of the solid below?
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第 4 章 立體圖形的探究 4.31 俯視 Top view 側視 Side view 正視 Front view A. B. C. D. □ 21. 下列哪一幅是以下正投影圖所表示的立 體之均角投影圖？ 21. Which of the following isometric projections represents a solid with an orthographic projection as shown?
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4.32 數學新里程 中三上 — 初中附加練習 俯視圖 Top view 側視圖 Side view 正視圖 Front view A. 俯視 Top view 側視 Side view 正視 Front view B. 俯視 Top view 側視 Side view 正視 Front view C. 俯視 Top view 側視 Side view 正視 Front view D. 俯視 Top view 側視 Side view 正視 Front view □
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第 4 章 立體圖形的探究 4.33 22. 下列哪一幅是以下正投影圖所表示的立 體之斜角投影圖？ 22. Which of the following oblique projections represents a solid with an orthographic projection as shown? 俯視圖 Top view 側視圖 Side view 正視圖 Front view A. 俯視 Top view 側視 Side view 正視 Front view B. 俯視 Top view 側視 Side view 正視 Front view C. 俯視 Top view 側視 Side view 正視 Front view
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4.34 數學新里程 中三上 — 初中附加練習 D. 俯視 Top view 側視 Side view 正視 Front view □ 下圖所示為正方體 ABCDEFGH 。 X 、 Y 和 Z 分別為 GH 、 EF 和 BC 的中點。試回答問題 23 26 。 The figure shows a cube ABCDEFGH . X , Y and Z are the mid-points of GH , EF and BC respectively. Answer the questions 23 – 26 . A B G H E F Y Z C X D 23. 下列哪一個是直角？ A. GAF B. BGA C. EDC D. BAG □ 23. Which of the following is a right angle? A. GAF B. BGA C. EDC D. BAG □ 24. 下列哪一個是線段 BG 和 AG 的相交角？ A. BAG B. AGB C. AXB D. GAZ □ 24. Which of the following is the angle between the line segments BG and AG ? A. BAG B. AGB C. AXB D. GAZ □
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第 4 章 立體圖形的探究 4.35 25. 下列哪一個是線段 AX 和平面 EFGH 的 相交角？ A. AFX B. AXF C. AXZ D. AXY □ 25. Which of the following is the angle between the line segment AX and the plane EFGH ? A. AFX B. AXF C. AXZ D. AXY □ 26. 下列哪一個是平面 AGH 和平面 BCHG 的相交角？ A. AXZ B. AGF C. AXY D. AGB □ 26. Which of the following is the angle between the planes AGH and BCHG ? A. AXZ B. AGF C. AXY D. AGB □
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