Creation of this resource was inspired by [url=http://www.gogeometry.com/problem/p231_triangle_midpoint_transversal_perpendicular.htm]this problem[/url] posted by [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]You can move the vertices of the triangle anywhere you'd like at any time. [br]You can also change the location of the (soon-to-appear) [b]LARGE POINT[/b] outside the triangle. [br][br][b]How can we formally prove what is dynamically illustrated here? [br][/b][br]Move the [b]LARGE POINT (outside the triangle)[/b] 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?