GoGeometry Action 173!

Creation of this resource was inspired by a problem posted by Antonio Gutierrez (GoGeometry). You can move the LARGE WHITE VERTICES of the white triangle anywhere you'd like at any time. Note: In this animation, dashed lines (soon-to-appear) are parallel to segments to which they appear to be. Questions: How can we put into words what is dynamically illustrated here? How can we formally prove this phenomenon always holds true for this special triangle?

Quick (Silent) Demo