Part 1: Constructing a Pedal Triangle:
Step 1: Draw a triangle.
Step 2: Pick a point anywhere and name that the Pedal Point, the point can be inside or outside of the triangle.
Step 3: Draw perpendicular lines from the pedal point to the three sides of the triangle and mark the intersection points.
Step 4: The pedal triangle is constructed using the three intersection points.
Part 2: Explore the Pedal Triangle:
To explore the Pedal Triangle and how is changes as you move the Pedal Point, use the Pedal Triangle GSP script tool.
Explorations:
1. Construct the centroid of the triangle and explore the Pedal Triangle when the Pedal Point is merged with the centroid.
2. Construct the Orthocenter and explore the Pedal Triangle when the Pedal Point is merged with the Orthocenter.
3. Construct the Incenter and explore the Pedal Triangle when the Pedal Point is merged with the Incenter.