Review of Perpendicular and Angle Bisectors in Triangles

Equidistant from the vertices of the triangle

The three perpendicular bisectors of each side meet at the circumcenter

Equidistant from the sides of the triangle

The three angle bisectors of each vertex meet at the incenter

2/3rds of the way from the vertices of the triangle to the midpoint of the opposite side (medians)

Because we know the midpoint's location for each side, we know that on either side of the midpoint, the segments are congruent.

Can also be found by taking the average of all the vertices

Where at least 2 perpendicular lines from the vertices of the triangle to the opposite side (altitudes) meet.

The orthocenter of an obtuse triangle is the only center that's OUTSIDE the triangle itself!