Example Intersection of a Line with a Pyramid

Example: Intersection of a Line with a Pyramid 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: Intersection of a Line with a Pyramid a) A pyramid is intersected by a line g [PQ]. Determine its plan and front view. S‘‘ Choose an auxiliary plane through the line g, which intersects the pyramid along simple lines. P‘‘ An auxiliary plane through the vertex intersects the pyramid along generatrices. Q‘‘ A‘‘ C‘‘ B‘‘ Define the intersection line of the auxiliary plane with the basement of the pyramid. C‘ p 1’’ = p 2’ S‘ A‘ Q‘ P‘ B‘ 2

Example: Intersection of a Line with a Pyramid a) A pyramid is intersected by a line g [PQ]. Determine its plan and front view. S‘‘ Define the intercepts of the intersection line with the basement of the pyramid. P‘‘ Define the according generatrices of the pyramid through these intercepts. Construct the intercepts of these generatrices with line g. Q‘‘ A‘‘ C‘‘ B‘‘ C‘ p 1’’ = p 2’ S‘ A‘ Q‘ P‘ B‘ 3

Example: Intersection of a Line with a Pyramid a) A pyramid is intersected by a line g [PQ]. Determine its plan and front view. S‘‘ Show proper visibility of line g with respect to the pyramid. P‘‘ Q‘‘ A‘‘ C‘‘ B‘‘ C‘ p 1’’ = p 2’ S‘ A‘ Q‘ P‘ B‘ 4

Example: Intersection of a Line with a Pyramid a) A pyramid is intersected by a line g [PQ]. Determine its plan and front view. S‘‘ Show proper visibility of line g with respect to the pyramid. P‘‘ Q‘‘ A‘‘ C‘‘ B‘‘ C‘ p 1’’ = p 2’ S‘ A‘ Q‘ P‘ B‘ 5

Example: Intersection of a Line with a Pyramid b) A pyramid is intersected by a line g [PQ]. Determine its plan and front view. Choose an auxiliary plane through the line g, which intersects the pyramid along simple lines. An auxiliary plane through the vertex intersects the pyramid along generatrices. Define the intersection line of the auxiliary plane with the basement of the pyramid. S‘‘ P‘‘ Define the intercepts of the intersection line with the basement of the pyramid. Define the according generatrices of the pyramid through these intercepts. Q‘‘ p 1’’ = p 2’ Construct the intercepts of these generatrices with line g. P‘ S‘ Q‘ 6

Example: Intersection of a Line with a Pyramid b) A pyramid is intersected by a line g [PQ]. Determine its plan and front view. S‘‘ Show proper visibility of line g with respect to the pyramid. P‘‘ Q‘‘ p 1’’ = p 2’ P‘ S‘ Q‘ 7