Medial triangle
= Medial triangle
The medial <triangle> joins the three <midpoints> of a <triangle>'s sides. Each side is parallel to the corresponding original side and has half its length: $((\mathbf x+\mathbf z)/2)-((\mathbf x+\mathbf y)/2)=(\mathbf z-\mathbf y)/2$. Each <altitude of a triangle> in the medial <triangle> is a <perpendicular bisector> of an original side, so its <orthocenter> is the original <triangle>'s <circumcenter>.