Most Used Theorems, Postulates, Definitions, etc.

1) Two points determine a line.
2) Three noncollinear points determine a plane.
3) If 2 lines intersect, then their intersection is a point.
4) If 2 planes intersect, then their intersection is a line.
5) Through a line and a point not on that line, there is exactly 1 plane.
6) Ruler Postulate -  
7) Segment Addition Postulate -  
8) Protractor Postulate -
9) Angle Addition Postulate -
10) Vertical Angle Theorem - Vertical angles are congruent.
11) Congruent Supplements Theorem - If two angles are supplements of congruent angles ( or the same angle), then the two angles are congruent.
12) Congruent Complements Theorem - If two angles are complements of congruent angles ( or the same angle), then the two angles are congruent.
13) Triangle - Angle - Sum Theorem - The sum of the interior angles of a triangle is 180.
14) Exterior Angle Theorem - The exterior angle of a triangle is equal to the sum of its remote interior angles.
15) Arc Addition Postulate -
16) Two sides of a triangle are congruent if and only if the angles opposite them are congruent.
17) The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of its base.
18) A triangle is equilateral if and only if it is equiangular.
19) If a triangle is a right triangle, then the acute angles are complementary.
20) If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent.
21) All right angles are congruent.
22) If two angles are supplementary and congruent, then each angle is a right angle.
23) Triangle Midsegment Theorem - If a segment joins the midpoints of two sides of a triangle, then the segment formed is parallel to the third side and one-half its length.
24) Perpendicular Bisector Theorem and Converse - A point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment.
25) Angle Bisector Theorem and Converse - A point is on the bisector of an angle if and only if it is equidistant from the sides of the angle.
26) Corresponding Angle Postulate - If two parallel lines are cut by a transversal, then corresponding angles are congruent.
27) Alternate Interior Angle Theorem - If two parallel lines are cut by a transversal, then alternate interior angles are congruent.
28) Same - Side Interior Angle Theorem - If two parallel lines are cut by a transversal, interior angles on the same side of the transversal are supplementary.
29) Converse of the Corresponding Angle Postulate - If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
30) Converse of the Alternate Interior Angle Theorem - If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
31) Converse of the Same - Side Interior Angle Theorem - If two lines are cut by a transversal so that same side interior angles are supplementary, then the lines are parallel.
32) SSS - If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
33) SAS - If two sides and an included angle of one triangle are congruent to two sides and an included angle of another triangle, then the triangles are congruent.
34) ASA - If two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the triangles are congruent.
35) AAS - If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
36) HL - If the hypotenuse and a leg of one right triangle are congruent to a corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.
37) Opposite sides of a parallelogram are congruent.
38) Opposite angles of a parallelogram are congruent.
39) Diagonals of a parallelogram bisect each other.
40) If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
41) If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. 
42) If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.
43) If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
44) If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
45) Diagonals of a rhombus bisect the rhombus's angles.
46) Diagonals of a rhombus are perpendicular.
47) Diagonals of a rectangle are congruent.
48) Base angles of an isosceles trapezoid are congruent.
49) Diagonals of an isosceles trapezoid are congruent.
50) Diagonals of a kite are perpendicular.