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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 A1B1C1are proportional to the sides of the original triangle, ABC is similar to  A1B1C1:




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