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Perpendicularity in Plane Geometry

Learn how lines perpendicular to planes behave in various views. Discover slopes and directions of planes, intersecting points, and visibility rules. Master the concepts step by step.

richardmackey
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Perpendicularity in Plane Geometry

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  1. Line Perpendicular to a Plane • A line perpendicular to a plane will appear perpendicular to the edge view of the plane. • A line perpendicular to a plane will appear true length in the edge view of the plane. • A line perpendicular to a plane is perpendicular to all lines in the plane. • Two perpendicular lines will appear perpendicular in a view that shows the TL of at least one of the lines.

  2. Steps: • Find the Edge View of the plane. • Construct a line from Point O, perpendicular to the EV. • Project Point O back to the original views. • Show correct visibility of the line in all views.

  3. Slope and Slope Direction of a Plane • Slope of a plane is the angle between the edge view of the plane and the horizontal reference plane (H). • Procedure: Find the edge view off the top view. (Find the point view of a line that is TL in the top view). Slope direction - direction of line/s of steepest slope - perpendicular to the direction of horizontal lines

  4. Piercing Point by Edge View of the Plane • Intersection between a line a plane • Can be seen in the Edge View of the plane • intersection of edge view and the line • Visibility: • Plane can hide part of the line. Visibility of line changes at piercing point. • Compare relative distance/position of line and plane from the reference plane -- whichever is closer to the reference plane will be visible in the “previous” view.

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