# Find Intersection of Two Planes Using Their Poles

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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## Example

Find the line of intersection of two planes:

• Strike 012 degrees, Dip 60 degrees SE
• Strike 107 degrees, Dip 41 degrees SSW

They are shown in different colors to distinguish them.

 1. Plot the poles of the two desired planes. The corresponding great circles are shown as dashed lines. 2. Rotate the poles until they lie on the same great circle. Plot the pole of this great circle (blue). 3.  Make a tick mark to mark the trend. Count in along the vertical great circle to find the plunge. 4. Return the overlay to its original orientation and count off the trend. The two intersecting planes are shown in red and green, the great circle through the poles in blue.

The great circles are shown above to illustrate the relationships but it is not necessary to construct them at all. in fact, a variation on this construction is used in analyzing folds, and in that case the diagram would be hopelessly cluttered if the great circles were to be shown. The same construction is shown below using only poles.

 1. Plot the poles of the two desired planes.  2. Rotate the poles until they lie on the same great circle. Plot the pole of this great circle (blue). 3.  Make a tick mark to mark the trend. Count in along the vertical great circle to find the plunge. 4. Return the overlay to its original orientation and count off the trend. The poles of the two intersecting planes are shown in red and green, the intersection of the two planes in blue.

## Why It Works:

• The pole to plane 1 is perpendicular to every line in plane 1.
• The pole to plane 2 is perpendicular to every line in plane 2.
• The intersection of planes 1 and 2 is a line common to both planes.
• Therefore this line must be perpendicular to both poles.
• Therefore the intersection line is the pole to the plane containing poles 1 and 2.