1) Perpendicular Bisector Theorem – Each point on the perpendicular bisector of a segment is
equidistant from the two endpoints of the segment.
2) Concurrence of Perpendicular Bisectors – IN any triangle, the perpendicular bisectors of the
sides are concurrent.
3) Concurrence of Angle Bisectors – In any triangle, the angle bisectors are concurrent.
4) The Triangle Congruence Postulates – If two triangles share the following triplets of congruent
corresponding parts, the triangles are congruent.
* ASA
* SAS
* SSS
(AAS is also true, but only if the angles and side are in the same order in both triangles.)
5) Exterior Angle Theorem, Version 1 – The measure of the exterior angle of a triangle is greater
than the measures of either of the triangle’s two remote interior angles.
6) Exterior Angle Theorem, Version 2 – The measure of the exterior angle of a triangle is equal to
the sum of the triangle’s two remote interior angles.
7) The Vertical Angles Theorem – All vertical angles are congruent.
8) The AIP Theorem – If two lines form congruent alternate interior angles with a transversal, then
the lines are parallel.
9) AIP Corollary 1 – If two lines form congruent corresponding angles with a transversal, then the
lines are parallel.
10) AIP Corollary 2 – If two lines form congruent alternate exterior angles with a transversal, then
the lines are parallel.
11) AIP Corollary 3 – If two lines form supplementary consecutive (same-side interior) angles with a
transversal, then the lines are parallel.
12) AIP Corollary 4 – If two lines form supplementary same-side exterior angles with a transversal,
then the lines are parallel.
13) The PAI Theorem – If two parallel lines are cut by a transversal, then the alternate interior
angles are congruent. (This the converse of the AIP theorem)
The converse of each AIP corollary is also true.
14) The Parallel Postulate – If a point P is not on line l, exactly one line through P exists that is
parallel to l.
15) The Triangle Angle Sum Theorem – The sum of the measures of the angles of a triangle is 180
degrees.
16) The Unique Perpendicular Theorem – If a point P is not on line l, there is exactly one line
through P that is perpendicular to l.
17) If two angles are supplementary to congruent angles, then the angles are congruent to each
other.
18) Angle Addition Postulate – The measure of an angle is equal to the sum of the measures of its
parts.
mBAD  mBAC  mCAD
B
A
C
D