Constructing the Perpendicular Line Through a Point Not on the Line

Topic:Angles, Congruence, Constructions, Geometry, Straight Lines

Use compass and ruler to draw on paper the construction described in the app below.

Try It Yourself...

The following app is the same as the previous one, but now includes GeoGebra tools.

Verify with GeoGebra

Explore the entire construction in the app above, then use the GeoGebra tools to measure the angle between line

and line

to verify the construction numerically. (Use the Undo and Redo buttons at the top right of the toolbar, or refresh the browser page to delete possible objects you have created but that are not useful or correct).

Consider the construction above and draw the segments and . The segment is the ______________ of the circle passing through and . What can you say about the lengths of the other segments that you have drawn? What geometric shape is polygon ? Why can we conclude that is perpendicular to ?

When are two intersecting lines said to be perpendicular?

Which symbol is used to indicate perpendicularity?

How many perpendicular lines to a given line pass through a point P not on the given line?

Define the (orthogonal) projection of a segment onto a line, then draw the projections of the segments on the line in the figure below.

Define the distance between a point and a line, then draw the distance between point P and line r in the figure below.

Constructing the Perpendicular Line Through a Point Not on the Line

Try It Yourself...

Verify with GeoGebra

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