Descriptive Geometry CH10 : PERPENDICULARITY

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.

Perpendicularity

Perpendicular Nonintersecting Lines • If 2 lines are ┴, they appear ┴ in any view showing at least

one of the lines in TL.

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.

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…

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.

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.

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.

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

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

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

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.

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

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

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

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.

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

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

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

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

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

Problem 10d. • Represent a plane that contains point O and is

perpendicular to line MN. Use the 2-view method.

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

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

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

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

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

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.

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.

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.

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.

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.

Problem 10k. • Locate the views of the shortest branch connecting pipes

MN & XY.