Aim: To prove that the perpendicular bisectors of the sides of the original triangle ABC are the same as the altitudes of the medial triangle DEF.

A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of (left figure). The perpendicular bisector of a line segment can be constructed using a compass by drawing circles centered at and with radius and connecting their two intersections.

 

An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude.

Sorry for the late post fellow classmates my internet went down.