GoGeometry Action 185!

Creation of this resource was inspired by this problem posted by Antonio Gutierrez. You can move the vertices of the triangle anywhere you'd like at any time. You can also change the location of the (soon-to-appear) LARGE POINT outside the triangle. How can we formally prove what is dynamically illustrated here? Move the LARGE POINT (outside the triangle) so the perpendicular segment from the triangle's vertex is not the longest of the 3 perpendicular segments. How can we always prove the lengths of the shorter 2 perpendiculars always sum to the length of the longest perpendicular segment?

Quick (Silent) Demo