Proofs

Isosceles Triangle Theorem (ITT)

If the sides of a triangle are congruent, then the opposite angles are congruent

Converse Isosceles Triangle Theorem (CITT)

If the angle of a triangle are congruent, then the opposite sides are congruent

Median

A segment from a vertex to the midpoint of the opposite side

Centroid

The place where all three of the medians of a triangle intersect

Altitude

A segment from a vertex perpendicular to the opposite side

Orthocenter

The place where all three of the altitudes of a triangle intersect

Perpendicular Bisector

A ray/segment/line that is perpendicular to the segment at its midpoint

Circumcenter

The place where all three perpendicular bisectors of a triangle intersect

Points of Concurrency

Where three or more lines meet at a common point (centroid, incenter, orthocenter, circumcenter)

Incenter

The place where all three angle bisectors of a triangle intersect