Question

4). Suppose that a Simson line of a triangle is parallel to one of the sides of the triangle. Show that the pole of this line must be one of the vertices of the triangle.

          4). Suppose that a Simson line of a triangle is parallel to one of the sides of the triangle.
Show that the pole of this line must be one of the vertices of the triangle.

Added by Joshua J.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

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Solved by Expert Donya Dobbin

Step 1

2) Let X, Y, and Z be the feet of the perpendiculars from P to the sides BC, CA, and AB, respectively. 3) The Simson line of P with respect to triangle ABC is the line passing through X, Y, and Z. 4) Suppose that the Simson line of P is parallel to one of the Show more…

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notice, it says parallel, please show proof. I will upvote. 4). Suppose that a Simson line of a triangle is parallel to one of the sides of the triangle Show that the pole of this line must be one of the vertices of the triangle.