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Similarity of Pedal Triangles

Karyn Carson

First,
letŐs start with triangle ABC,

and
insert point P inside the triangle:

Next,
construct perpendicular lines through P and each side of triangle ABC:

then
create segments from P to each of the intersections and hide each of the
original perpendicular lines:

Construct
a triangle, with each intersection becoming a vertex of the new triangle and
hide the perpendicular segments:

This is
called the pedal triangle.

Construct
two more pedal triangles, using the same point P:

Because the sides of the resulting triangle A_{1}B_{1}C_{1}are
proportional to the sides of the original triangle, ABC is similar to A_{1}B_{1}C_{1:}

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