Example Truncated Pyramid Surface Cut by Prism Additional

Example: Truncated Pyramid (Surface) Cut by Prism Additional Task to the multimedia book „Darstellende Geometrie/ 3 D-Geometry“, published by Veritas Educational Edition Student Edition ISBN - 978 -3 -7058 -9079 -4 ISBN - 978 -3 -7058 -9293 -4 Special edition for teachers: The print version shows handouts of theory and worked-out examples. Each handout can be printed in colour and is also suitable as a solutions handout. Through the use of animated Power. Point files it is possible to structure the lessons in a contemporary and innovative manner for students. Special edition for students: The print version consists of well prepared worksheets to start working right away. On the CD you will find colourful Power. Point presentations, including theory as well as solved examples with step-by-step explanations. This provides a highly efficient technique in developing an understanding of geometry and its concepts. for more DETAILS and ORDER 1

Example: Truncated Pyramid (Surface) Cut by Prism A given surface of a truncated pyramid is cut by a straight prism. The prism is given by its cross-section (=square), that lies in the plane of symmetry of the pyramid. Complete the intersection polygon and show proper visibility of the remaining surface. Define plane of symmetry of the pyramid, by locating midpoint of its basement. S Show the square in the plane of symmetry. D 1 C 1 D C A B 2

Example: Truncated Pyramid (Surface) Cut by Prism A given surface of a truncated pyramid is cut by a straight prism. The prism is given by its cross-section (=square), that lies in the plane of symmetry of the pyramid. Complete the intersection polygon and show proper visibility of the remaining surface. Define the intersection of the top face of the truncated pyramid with this vertical plane of symmetry. S Extrude the profile of the straight prism along its (intersecting) edges. D 1 C 1 D C A B 3

Example: Truncated Pyramid (Surface) Cut by Prism A given surface of a truncated pyramid is cut by a straight prism. The prism is given by its cross-section (=square), that lies in the plane of symmetry of the pyramid. Complete the intersection polygon and show proper visibility of the remaining surface. S Show the visibility remaining part of the skew top face of the truncated pyramid. D 1 C 1 D C A B 4

Example: Truncated Pyramid (Surface) Cut by Prism A given surface of a truncated pyramid is cut by a straight prism. The prism is given by its cross-section (=square), that lies in the plane of symmetry of the pyramid. Complete the intersection polygon and show proper visibility of the remaining surface. S Define further points of the intersection polygon. Use an auxiliary plane, that is parallel to lateral side of the prism. D 1 C 1 D C A B 5

Example: Truncated Pyramid (Surface) Cut by Prism A given surface of a truncated pyramid is cut by a straight prism. The prism is given by its cross-section (=square), that lies in the plane of symmetry of the pyramid. Complete the intersection polygon and show proper visibility of the remaining surface. Connect appropriate points of the intersecting polygon. S Show proper visibility of the remaining surface. D 1 C 1 D C A B 6