Exploration 9: Write-Up

The Pedal Triangle:

For a triangle ABC and a point P, there is a triangle that can be constructed by constructing perpendicular lines through P and each side of triangle ABC. The intersections of the perpendicular lines form the triangle RST.

Here is an example of the pedal triangle:

More specifically, this is the pedal triangle created when p is a point in the plane but outside of the circle.

Click Here to manipulate the Pedal Triangle in GSP.

What happens to the pedal triangle when the point P is placed at one one of the vertices?

From the images to the left it can be seen that as the point P is placed on each vertex, the triangle seems to dissolve and become a straight line going through the vertex and a point on the opposite side.

What happens when the point P is placed on one of the sides?

We can see that when the point P is located on a segment of triangle ABC, it follows that a triangle will be created which is located within the triangle ABC.


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