Example C Intersection Line of Two Triangles Additional

Example C: Intersection Line of Two Triangles Determine the intersection segment of triangle ABC

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Example C: 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 C: Intersection Line of Two Triangles Determine the intersection segment of triangle ABC and triangle PQR in the plan view- use method of cover line. Show proper visibility. P‘‘ B‘‘ NOTE: All intercepts Si of lines of plane α with plane β are collinear and therefore lie on the intersection line of these two planes. 2‘‘ R‘‘ S 1‘‘ Choose any auxiliary line, which covers one side (e. g. PQ) of a triangle in e. g. the plan view. LOCATE that auxiliary line, as a line of the opposite triangle, i. e. triangle ABC. Q‘‘ 1‘‘ A‘‘ p 1‘‘=p 2‘ Q‘ C‘ 2‘ This auxiliary line is a line of plane ABC and intersects line PQ in the required intercept S 1‘ B‘ 1‘ R‘ P‘ Solve the same task in the axonometric view → A‘ 2

Example C: Intersection Line of Two Triangles Determine the intersection segment of triangle ABC and triangle PQR in the plan view- use method of cover line. Show proper visibility. P‘‘ B‘‘ Define second intercept: Choose a further auxiliary line, which covers another side (e. g. AB) of the triangle in e. g. the plan view. 2‘‘ R‘‘ S 1‘‘ S 2‘‘ C‘‘ LOCATE that auxiliary line, as a line of the opposite triangle, i. e. triangle PQR. This auxiliary line is a line of plane PQR and intersects line AB in the required intercept S 2. 3‘‘ 4‘‘ Q‘‘ 1‘‘ A‘‘ p 1‘‘=p 2‘ Q‘ C‘ 2‘ The intercepts S 1 and S 2 define the required intersection line. B‘ S 1‘ 4‘ 1‘ S 2‘ R‘ 3‘ P‘ Solve the same task in the axonometric view → A‘ 3

Example C: Intersection Line of Two Triangles Determine the intersection segment of triangle ABC and triangle PQR in the plan view- use method of cover line. Show proper visibility. P‘‘ B‘‘ s ‘‘ Show proper visibility of these two triangles and their intersection. The intersection segment of these triangle is a segment, which lies within both triangles and is visible at all. 1 2‘‘ 3‘‘ R‘‘ S 1‘‘ S 2‘‘ C‘‘ Define the visibility in the plan view. One virtual intercept lies either on QR or on CB. Q‘‘ 1‘‘ At the virtual intercepts the visibility may change. Locate these points in the front view. 4‘‘ A‘‘ p 1‘‘=p 2‘ Q‘ C‘ 2‘ The virtual intercept on CB is nearer to the corresponding lines of sight, therefore line CB lies in front of QR in the plan view. B‘ S 1‘ 4‘ 1‘ S 2‘ R‘ 3‘ P‘ Solve the same task in the axonometric view → A‘ 4

Example C: Intersection Line of Two Triangles Determine the intersection segment of triangle ABC and triangle PQR in the plan view- use method of cover line. Show proper visibility. P‘‘ B‘‘ s ‘‘ 1 Show proper visibility of these two triangles and their intersection. Define further virtual intercept PQ with AC in the front view. The point on PQ lies higher (closer the respective lines of sight), thus line AC lies below PQ at this position. Complete the visibility in the plan view. Notice: visibility must change at the intersection segment. 2‘‘ 3‘‘ R‘‘ S 1‘‘ S 2‘‘ C‘‘ 4‘‘ Q‘‘ 1‘‘ A‘‘ p 1‘‘=p 2‘ Q‘ C‘ 2‘ B‘ S 1‘ 4‘ 1‘ S 2‘ R‘ 3‘ P‘ Solve the same task in the axonometric view → A‘ 5