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Similarity of Pedal Triangles

Karyn Carson

 

First, let’s 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  A₁B₁C_1:

 

 

 

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