HG 35
T56. The perpendicular bisector of any side of a triangle is perpendicular to the line which bisects the other sides.
T57. A line which bisects a side of a triangle and is perpendicular to the perpendicular bisector of another side also bisects the third side.
T58. The line joining the midpoints of the summit and base of a SQ is shorter than each leg.
T59. If two parallels have a common perpendicular, then they cannot have a second one.