Hello ,
a random point was chosen on side of triangle . Point is the center of side . Segments and meet at . Point is the center of segment , while point lies on and . Show that is parallel to .
It's gotten too complicated for me. I'm hoping for your kind help.
Here's a possible geometric starting point,
working from the symmetry and utilising the fact that the midpoint
of two sides is chosen, causing the small triangles to be congruent.
The lines being parallel causes |BS|=|QT|.
The converse is then true.
The third side of the triangle can then be added
(left out for clarity).