desn 106 -36n descriptive geometry - faculty...
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![Page 1: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/1.jpg)
Descriptive Geometry CH10 : PERPENDICULARITY
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Perpendicularity • If a line is ┴ to a plane, it is ┴ to every line in the plane. • EF & GJ are intersecting ┴ lines. • YX & GJ are nonintersecting ┴ lines.
![Page 3: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/3.jpg)
Perpendicularity
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Perpendicular Nonintersecting Lines • If 2 lines are ┴, they appear ┴ in any view showing at least
one of the lines in TL.
![Page 5: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/5.jpg)
Test for Perpendicularity • If it is not evident from an existing view, construct an auxiliary
view showing one of the lines in TL (like MN) to see if the lines are ┴ in space.
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Create a Plane Perpendicular to Line 1. Evaluate the given problem
& find or create a view of the line (gj) in TL.
2. Create a new plane through the point (e), where the line of the EV is ┴ to the line (gj)
3. Project the new plane into all views…
![Page 7: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/7.jpg)
Create a Plane Perpendicular to Line 3. Project the new plane into all
views…
1) Establish any random pair of points in the new plane, like k & m.
2) In the front view, place the new points anywhere along their projection lines. Locate them in the top view according to their distance from the FL in the auxiliary.
![Page 8: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/8.jpg)
Create a Plane Perpendicular to Line 1. Evaluate the given problem & find or
create a view of the line (gj) in TL
2. Create a new plane through the point (e), where the line of the EV is ┴ to the line (gj)
3. Project the new plane into all views…
1) Establish any random pair of points in the new plane, like k & m.
2) In the front view, place the new points anywhere along their projection lines. Locate them in the top view according to their distance from the FL in the auxiliary.
![Page 9: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/9.jpg)
Create a Plane Perpendicular to Line 1. Evaluate the given problem & find or
create a view of the line (gj) in TL
2. Create a new plane through the point (e), where the line of the EV is ┴ to the line (gj)
3. Project the new plane into all views…
1) Establish any random pair of points in the new plane, like k & m.
2) In the front view, place the new points anywhere along their projection lines. Locate them in the top view according to their distance from the FL in the auxiliary.
![Page 10: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/10.jpg)
Create a Line Perpendicular to Plane
1. Evaluate the given problem & find or create a TL line in the given plane
2. Create an EV of the plane from the TL line (LOS parallel)
3. Create a new line (ak) through the point (a), ┴ to the EV of the plane
4. Project the new line into all views…
5. Solve for visibility
![Page 11: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/11.jpg)
Create a Line Perpendicular to Plane
1. Evaluate the given problem & find or create a TL line in the given plane
2. Create an EV of the plane from the TL line (LOS parallel)
3. Create a new line (ak) through the point (a), ┴ to the EV of the plane
4. Project the new line into all views…
5. Solve for visibility
![Page 12: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/12.jpg)
Create a Line Perpendicular to Plane
1. Evaluate the given problem & find or create a TL line in the given plane
2. Create an EV of the plane from the TL line (LOS parallel)
3. Create a new line (ak) through the point (a), ┴ to the EV of the plane
4. Project the new line into all views…
5. Solve for visibility
![Page 13: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/13.jpg)
Create a Line Perpendicular to Plane 4. Project the new line into all views…
1) Establish any random points on the new line, like k.
2) In the adjacent view, find the new point (k) & the piercing point by drawing a line from A ┴ to the TL line. Extend the new line until it intersects the projection line of the new point (k).
3) Locate the new point & the piercing point in the final view according to their distance from the FL in the auxiliary.
![Page 14: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/14.jpg)
Create a Line Perpendicular to Plane
1. Evaluate the given problem & find or create a TL line in the given plane
2. Create an EV of the plane from the TL line (LOS parallel)
3. Create a new line (ak) through the point (a), ┴ to the EV of the plane
4. Project the new line into all views…
5. Solve for visibility
![Page 15: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/15.jpg)
Create a Line Perpendicular to Plane
1. Evaluate the given problem & find or create a TL line in the given plane
2. Create an EV of the plane from the TL line (LOS parallel)
3. Create a new line (ak) through the point (a), ┴ to the EV of the plane
4. Project the new line into all views…
5. Solve for visibility
![Page 16: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/16.jpg)
Create a Line Perpendicular to Plane
1. Evaluate the given problem & find or create a TL line in the given plane
2. Create an EV of the plane from the TL line (LOS parallel)
3. Create a new line (ak) through the point (a), ┴ to the EV of the plane
4. Project the new line into all views…
5. Solve for visibility
![Page 17: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/17.jpg)
Common Perpendicular • Connecting 2 skew (nonintersecting, nonparallel) lines is one
& only line which is ┴ to both – the common perpendicular. • The shortest distance from a point to a line is measured
along the ┴ from the point to the line.
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Common Perpendicular 1. Evaluate the given
problem & find or create a view of one of the lines (ab) as TL
2. Create an point view of the TL line (LOS parallel)
3. Create a new line through the point view (ab), ┴ to the second line (ce)
4. Project the new line into all views
![Page 19: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/19.jpg)
Common Perpendicular 1. Evaluate the given
problem & find or create a view of one of the lines (ab) as TL
2. Create an point view of the TL line (LOS parallel)
3. Create a new line through the point view (ab), ┴ to the second line (ce)
4. Project the new line into all views
![Page 20: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/20.jpg)
Common Perpendicular 1. Evaluate the given
problem & find or create a view of one of the lines (ab) as TL
2. Create an point view of the TL line (LOS parallel)
3. Create a new line through the point view (ab), ┴ to the second line (ce)
4. Project the new line into all views
![Page 21: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/21.jpg)
Common Perpendicular 1. Evaluate the given
problem & find or create a view of one of the lines (ab) as TL
2. Create an point view of the TL line (LOS parallel)
3. Create a new line through the point view (ab), ┴ to the second line (ce)
4. Project the new line into all views
![Page 22: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/22.jpg)
Common Perpendicular 1. Evaluate the given
problem & find or create a view of one of the lines (ab) as TL
2. Create an point view of the TL line (LOS parallel)
3. Create a new line through the point view (ab), ┴ to the second line (ce)
4. Project the new line into all views
![Page 23: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/23.jpg)
Problem 10d. • Represent a plane that contains point O and is
perpendicular to line MN. Use the 2-view method.
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Shortest Horizontal Line Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line (using a line parallel to the second line).
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to FL H/1. Where the 2 lines intersect is the point view of the shortest horizontal line connecting them.
5. Project the new line into all views
![Page 25: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/25.jpg)
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line (using a line parallel to the second line).
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to FL H/1. Where the 2 lines intersect is the point view of the shortest horizontal line connecting them.
5. Project the new line into all views
Shortest Horizontal Line Connecting 2 Skew Lines
![Page 26: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/26.jpg)
Shortest Horizontal Line Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line (using a line parallel to the second line).
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to FL H/1. Where the 2 lines intersect is the point view of the shortest horizontal line connecting them.
5. Project the new line into all views
![Page 27: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/27.jpg)
Shortest Horizontal Line Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line (using a line parallel to the second line).
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to FL H/1. Where the 2 lines intersect is the point view of the shortest horizontal line connecting them.
5. Project the new line into all views
![Page 28: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/28.jpg)
Shortest Horizontal Line Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line.
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to FL H/1. Where the 2 lines intersect is the point view of the shortest horizontal line connecting them.
5. Project the new line into all views
![Page 29: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/29.jpg)
Shortest Line at Specified Grade Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line.
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to 15% grade away from the H/1 FL. Where the 2 lines intersect is the point view of the line connecting them.
5. Project the new line into all views
• Find the shortest connecting line having a downward grade of 15% from line MN to OP.
![Page 30: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/30.jpg)
Shortest Line at Specified Grade Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line.
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to 15% grade away from the H/1 FL. Where the 2 lines intersect is the point view of the line connecting them.
5. Project the new line into all views
• Find the shortest connecting line having a downward grade of 15% from line MN to OP.
![Page 31: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/31.jpg)
Shortest Line at Specified Grade Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line.
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to 15% grade away from the H/1 FL. Where the 2 lines intersect is the point view of the line connecting them.
5. Project the new line into all views
• Find the shortest connecting line having a downward grade of 15% from line MN to OP.
![Page 32: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/32.jpg)
Shortest Line at Specified Grade Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line.
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to 15% grade away from the H/1 FL. Where the 2 lines intersect is the point view of the line connecting them.
5. Project the new line into all views
• Find the shortest connecting line having a downward grade of 15% from line MN to OP.
![Page 33: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/33.jpg)
Shortest Line at Specified Grade Connecting 2 Skew Lines
1. Evaluate the given problem & find or create a view of a line as TL (in the horiz view – i.e. create a horizontal line)
2. Create a plane from the given line & the TL line.
3. Create an EV of the plane (LOS parallel to the TL line)
4. Construct a 2nd auxiliary with a LOS parallel to 15% grade away from the H/1 FL. Where the 2 lines intersect is the point view of the line connecting them.
5. Project the new line into all views
• Find the shortest connecting line having a downward grade of 15% from line MN to OP.
![Page 34: DESN 106 -36N Descriptive Geometry - Faculty Webfaculty.ivytech.edu/~bl-desn/dsn106/images/WK07-CH10.pdfProblem 10d. • Represent a plane that contains point O and is perpendicular](https://reader030.vdocuments.mx/reader030/viewer/2022040719/5e292334d0b4a1406833d266/html5/thumbnails/34.jpg)
Problem 10k. • Locate the views of the shortest branch connecting pipes
MN & XY.