Example Intersection Line of Two Triangles Additional Task

Example: Intersection Line of Two Triangles 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 Line of Two Triangles Triangle ABC and PQR are given in an axonometric view. Use vertical auxiliary planes to determine the intersection curve of these planar figures. Show proper visibility of the intersecting triangles. Project all points into the xy- plane and label them appropriately. Connect all points in the xy-plane. B P R C Q Q’ x C’ z B’ R’ P’ y A’=A Solve the same task in principle views → 2

Example: Intersection Line of Two Triangles Triangle ABC and PQR are given in an axonometric view. Use vertical auxiliary planes to determine the intersection curve of these planar figures. Show proper visibility of the intersecting triangles. Choose vertical auxiliary plane through line PQ. This plane shows first edge view. and intersects plane ABC along line d. P Line d is covered by line PQ in the xy- plane. 2 R d Line d intersects C AC and BC in intercepts 1 and 2. Locate point 1 and 2 in the axonometric x view. B S 1 Q Q’ 1 C’ 2’ d‘ z B’ R’ y 1’ P’ A’=A Solve the same task in principle views → 3

Example: Intersection Line of Two Triangles Triangle ABC and PQR are given in an axonometric view. Use vertical auxiliary planes to determine the intersection curve of these planar figures. Show proper visibility of the intersecting triangles. Choose a vertical auxiliary plane through line AB. This plane shows first edge view. and intersects plane ABC along line e. P Line e is covered by line AB in the xy- plane. B 2 3 e d Line e intersects C PR and QR in intercepts 3 and 4. 4 S 1 Q Locate point 3 and 4 in the axonometric view. x R S 2 z Q’ 1 C’ B’ e‘ 4’ 2’ d‘ y 3’ 1’ P’ R’ A’=A Solve the same task in principle views → 4

Example: Intersection Line of Two Triangles Triangle ABC and PQR are given in an axonometric view. Use vertical auxiliary planes to determine the intersection curve of these planar figures. Show proper visibility of the intersecting triangles. Connect S 1 and S 2 to define the intersection line s of plane ABC with plane PQR. The required intersection segment must lie within both planar figures and is visible at all. B 2 P 3 e d C z Q’ 1 C’ B’ e‘ 4’ 2’ d‘ R’ y 3’ 1’ P’ 4 s S 1 Q x R S 2 A’=A Solve the same task in principle views → 5

Example: Intersection Line of Two Triangles Triangle ABC and PQR are given in an axonometric view. Use vertical auxiliary planes to determine the intersection curve of these planar figures. Show proper visibility of the intersecting triangles. B Show proper visibility. 2 P 3 e d C z Q’ 1 C’ B’ e‘ 4’ 2’ d‘ R’ y 3’ 1’ P’ 4 s S 1 Q x R S 2 A’=A Solve the same task in principle views → 6

Example: Intersection Line of Two Triangles Triangle ABC and PQR are given in an axonometric view. Use vertical auxiliary planes to determine the intersection curve of these planar figures. Show proper visibility of the intersecting triangles. B Show proper visibility. Hatch all visible parts of the planar figures to show a proper result. 2 P 3 e d C z Q’ 1 C’ B’ e‘ 4’ 2’ d‘ R’ y 3’ 1’ P’ 4 s S 1 Q x R S 2 A’=A Solve the same task in principle views → 7