Name of the Theorem

 Statement of the Theorem

Midpoint Theorem

 If M is the midpoint of AB, then AM ≅ MB. 
Ruler Postulate
  The points on any line or line segment can be paired with real numbers so that, given any points A and B on a line, A corresponds to zero,and B corresponds to a positive real number.

Segment Addition Postulate
  If B is between A and C, then AB + BC = AC. Conversely if AB + BC = AC, then B is between A and C.

Segment Congruence Theorem 
 Congruence of segments is reflexive, symmetric and transitive.

Protractor Postulate   Given $\overrightarrow{AB}$ and a number x between 0 and 180, there is exactly one ray with end point A, extending on either side of $\overrightarrow{AB}$ such that, the measure of the angle formed is xº.

Angle addition Postulate
  If D is in the interior of ∠ABC, them m ∠ABD + m ∠DBC = m ∠ABC Conversely if m ∠ABD + m ∠DBC = m ∠ABC, then D is in the interior of ∠ABC 
Supplement Theorem

 If two angles form a linear pair then they are supplementary angles. 
Complement Theorem

 If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary. 
Angle Congruence Theorem

 Congruence of angles is reflexive, symmetric and transitive. 
Vertical Angle Theorem
  If two angles are vertical, then they are congruent.

Corresponding angles Postulate
  If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.

Alternate Interior angles Theorem   If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. 
Consecutive interior angles Theorem
  If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.

Alternate Exterior angles Theorem   If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. 
Perpendicular Transversal Theorem   In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

Parallel Postulate
  If there is a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. 
Perpendicular Bisector Theorem
  If a point is equidistant from the end points of a segment, then it lies on the perpendicular bisector of the segment. Conversely a point on the perpendicular bisector of a segment is equidistant from the end points of the segment. 
Angle Sum Theorem
  The sum of the measures of the angles of a triangle is 180 degrees.

Third angle Theorem
  If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. 
Exterior angle Theorem
  The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

SideSideSide Congruence (SSS) Theorem
  If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

SideAngleSide Congruence (SAS) Theorem
  If two sides and included angle of one triangle are congruent to two sides and included angle of another triangle, then the two triangles are congruent.

AngleSideAngle Congruence (ASA) Theorem
  If two angles and included side of one triangle are congruent to two angles and included side of another triangle, then the two triangles are congruent. 
AngleAngleSide Congruence (AAS) Theorem   If two angles and a nonincluded side of one triangle are congruent to two angles and nonincluded side of another triangle, then the two triangles are congruent.

LegLeg Congruence (LL) Theorem
  If the legs of one right triangle are congruent to the legs of another right triangle, then the triangles are congruent.

HypotenuseLegCongruence (HL) Theorem   If the Hypotenuse and the leg of one right angle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

HypotenuseAngle Congruence (HA) Theorem
  If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent.

Leg Angle congruence (LA) Theorem   If one leg and an acute angle of a right triangle are correspondingly congruent to one leg and an acute angle of another right triangle, then the triangles are congruent. 
Isosceles Triangle Theorem
  If two sides of a triangle are congruent, then the angles opposite to those two sides are congruent. 
Exterior Angle Inequality Theorem
  If an angle is an exterior angle of a triangle, then its measure is greater than the either of its remote interior angles.

Triangle Inequality Theorem
  The sum of the lengths of any two sides of a triangle is greater than the third side.

SAS Inequality/Hinges Theorem
  If two sides of a triangle are congruent to the two sides of another triangle, and the included angle in one triangle has a greater measure than the included angle in the other, then the third side of the first triangle is longer than the third side of the second triangle.

SSS Inequality Theorem
  If two sides of a triangle are congruent to two sides of another triangle, and the third side in one triangle is longer than the third side in the other, then the angle opposite to the third side in the first triangle is greater than the corresponding angle in the second triangle.

AngleAngle (AA) Similarity
  If two angles of one triangle are congruent to two angles of another triangle then the triangles are similar.

SideSideSide (SSS) Similarity
  If the measures of corresponding sides of two triangles are proportional, then the two triangles are similar. 
SideAngleSide (SSS) Similarity.
  If the measures of two sides of a triangle are proportional to the measures of the two sides of another triangle, and the included angles are congruent, then the two triangles are congruent. 
Triangle Proportionality Theorem   If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these two sides into segments of proportional lengths.

Converse of the Triangle Proportionality Theorem   If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side. 
Midsegment Theorem
  A Midsegment of a triangle is parallel to one side of a triangle and its length is onehalf the length of that side.

Angle Bisector Theorem
  An angle bisector in a triangle separates the opposite sides into segments in the same ratio as the other two sides. 
Pythagorean Theorem
  In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.

Converse of the Pythagorean Theorem
  If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

Interior Angle Sum Theorem
  The sum of the measures of the interior angles of a convex polygon of n sides = 180(n 2) degrees. 
Exterior angle Sum Theorem   The sum of the measures of the exterior angles, one at each vertex of a convex polygon is 360 degrees.
