Example Intersection Line of Two Planes Additional Task

Example: Intersection Line of Two Planes 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 Planes The axonometric view of a triangle ABC and a parallelogram PQRS are given. Determine the intersection segment of these figures and show proper visibility. Complete parallelogram PQRS. Label all points in the auxiliary view- plan view. Connect appropriate points ABC and PQRS in the auxiliary view. S P C z B C’ P’ S’ A’=A R Q y Q’ x R’ B’ Solve the same task in principle views → 2

Example: Intersection Line of Two Planes The axonometric view of a triangle ABC and a parallelogram PQRS are given. Determine the intersection segment of these figures and show proper visibility. Choose a vertical auxiliary plane through line PQ. This plane is imaged as an edge in the plan view. The auxiliary plane intersects plane ABC along line d, which covers PQ in the plan view. C Line d intersects line AB and AC in intercepts 1 and 2. Locate intercepts 1 and 2 in the axonometric view. S P z B 2 S 1 P’ A’=A x 2’ d 1 C’ S’ R Q d‘ Q’ y 1’ R’ B’ Solve the same task in principle views → 3

Example: Intersection Line of Two Planes The axonometric view of a triangle ABC and a parallelogram PQRS are given. Determine the intersection segment of these figures and show proper visibility. Choose a vertical auxiliary plane through line BC. This plane is imaged as an edge in the plan view. The auxiliary plane intersects plane PQRS along line e, which covers CB in the plan view. S C S 2 Line d intersects line QRand PS in intercepts 3 and 4. Locate intercepts 3 and 4 in the axonometric view. 3 P z B 2 S 1 P’ 2’ A’=A x e d 1 C’ S’ 3’ Q d‘ Q’ R 2 y e‘ 1’ 4’ R’ B’ Solve the same task in principle views → 4

Example: Intersection Line of Two Planes The axonometric view of a triangle ABC and a parallelogram PQRS are given. Determine the intersection segment of these figures and show proper visibility. Connect S 1 and S 2 to define the intersection line of these two planes. The required intersection segment is defined by that part which lies within both faces (ABC and PQR). This segment is visible at all. 3 P S s C S 2 z B 2 S 1 d P’ 2’ A’=A x e 1 C’ S’ 3’ Q d‘ Q’ R 2 y e‘ 1’ 4’ R’ B’ Solve the same task in principle views → 5

Example: Intersection Line of Two Planes The axonometric view of a triangle ABC and a parallelogram PQRS are given. Determine the intersection segment of these figures and show proper visibility. Show proper visibility. 3 P S s C S 2 z B 2 S 1 d P’ 2’ A’=A x e 1 C’ S’ 3’ Q d‘ Q’ R 2 y e‘ 1’ 4’ R’ B’ Solve the same task in principle views → 6

Example: Intersection Line of Two Planes The axonometric view of a triangle ABC and a parallelogram PQRS are given. Determine the intersection segment of these figures and show proper visibility. Show proper visibility. 3 P S s C S 2 z B 2 S 1 d P’ 2’ A’=A x e 1 C’ S’ 3’ Q d‘ Q’ R 2 y e‘ 1’ 4’ R’ B’ Solve the same task in principle views → 7