This is a partial listing of the more popular rules (theorems, postulates, and properties) that you will be using in your study of Geometry.

 First a few words that refer to types of geometric "rules": • A theorem is a statement (rule) that has been proven true using facts, operations and other rules that are known to be true. These are usually the "big" rules of geometry. A short theorem referring to a "lesser" rule is called a lemma. • A corollary is a follow-up to an existing proven theorem. Corollaries are off-shoots of a theorem that require little or no further proof. • A postulate (or axiom) is a statement (rule) that is taken to be true without proof. Euclid derived many of the rules for geometry starting with a series of definitions and only five postulates. • A property is a quality or characteristic belonging to something. For example, the real numbers have the associative, commutative and distributive properties.

 Your textbook (and your teacher) may want you to remember these "rules" with slightly different wording. Be sure to follow the directions from your teacher.

Angles:

 Two angles that share a common vertex, a common side, and no common interior points (don't overlap). m∠ABD and m∠DBC are adjacent. m∠ABC and m∠DBC are not adjacent
Linear Pair
Two adjacent angles whose non-common sides for a straight line.
Straight Angles
All straight angles are congruent (equal in measure).
(They all have a measure of 180º.)
Vertical Angles
 Vertical angles are congruent (equal in measure). m∠1 = m∠2 m∠3 = m∠4
Triangle Interior Sum
The sum of the measures of the interior angles of a triangle is 180º.
Exterior Angle
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
Angles forming a straight line
Angles around a point
Complementary Angles
Two angles the sum of whose measures is 90º.
Supplementary Angles
Two angles the sum of whose measures is 180º.

Triangles:

 Pythagorean Theorem c2 = a2 + b2 In a right triangle, the square of the hypotenuse equals the sum of the square of the lengths of the legs. Sum of Two Sides The sum of the lengths of any two sides of a triangle must be greater than the third side. Longest Side In a triangle, the longest side is across from the largest angle. Largest Angle In a triangle, the largest angle is across from the longest side Congruent Triangles Triangles that are congruent if there corresponding angles are congruent and their corresponding sides are congruent. Short-cuts to verify congruent triangles SSS, ASA, AAS, SAS, HL(in right triangles) Angle-Angle (AA) Similarity If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Sides of Similar Δs Corresponding sides of similar triangles are in proportion.

Parallels:

 Corresponding Angles If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Alternate Interior Angles If two parallel lines are cut by a transversal, then the alternate interior angles are congruent. Alternate Exterior Angles If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent. Interiors on Same Side If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.
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