# Investigation Nine

# Pedal Triangles

### Charles Meyer

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### In this investigation I will look at the pedal triangle. Along
the way I hope to educate the reader on its orgins as well as
its different properties.

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### A pedal triangle is formed from the perpendiculars of a given
triangle to a point P in the plane, then the intersection of triangle
ABC to the perpendiculars will form a triangle.

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### Let's begin with the triangle ABC and Point B.

### Now we must create the perpendiculars from each segment of
ABC to point P.

### The intersections of the segments and the perpendiculars are
now found and labeled TSR so that the triangle TSR is the pedal
triangle of point P.

### Below are example of the the point P being within different
parts of the triangle. There is not much overall difference to
the triangle at the different points other than size of interior
angles.

### What is really fascinating is the fact that the point P can
also lie outside the triangle as shown below and still a triangle
can be found.

### However at some point the triangle is lost as the perpendicular
intersections are unable to form a triangle.

### The study of pedal triangles may be helpful to high school
geometry students who are trying to find interesting parts of
triangle construction.

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