Honors Geometry Cheat Sheet

Unit 1

Line Postulate: There exists exactly one line through any two points

Plane Postulate: There exists exactly one plane through any 3 noncollinear points

Segment Addition Postulate: If points A, B, and C are on the same line with B between A and C, then AB + BC = AC

Definition of Congruence: If segment AM = segment MB, then AM is congruent to MB; If m<CBD = m<XYZ, then <CBD is congruent to <XYZ

Definition of Angle Bisector: A ray that divides an angle into two congruent angles

Definition of Midpoint: If M is the midpoint of AB then AM is congruent to MB

Law of Detachment: If p -> q is a true statement and p is true, then q is true

Law of Syllogism: If p -> q and q -> r are true statements, then p -> r is a true statement

Add POE: If a = b, then a + c = b + c

Subtraction POE: If a = b, then a - c = b - c

Mult POE: If a = b, then a x c = b x c

Division POE: If a = b and c =/ 0, then a/c = b/c

Reflexive POE: a = a

Symmetric POE: If a = b, then b = a

Transitive POE: If a = b and b = c, then a = c

Substitution POE: If a = b, then a may be replaced by b in any expression/equation

Distributive POE: a(b+c) = ab + ac

Associative POAdd: (a+b) + c = a + (b + c)

Associative POMult: (ab)c = a(bc)

Commutative POAdd: a + b = b + a

Commutative POMult: ab = ba

Additive Identity: a + 0 = a = 0 + a

Multiplicative Identity: a x 1 = 1 x a

Additive Inverse: a + (-a) = 0 = (-a) + a

Multiplicative Inverse: a x 1/a = 1/a x a if a =/ 0

Multiplication Prop of Zero: a x 0 = 0 = 0 x a

Zero Product Property: If ab = 0, then a = 0 or b = 0

Vertical Angles Theorem: If two angles are vertical angles, then they are congruent

Congruent Supplements Theorem: Angles supplementary to the same angle or to congruent angles are congruent

Congruent Complements Theorem: Angles complementary to the same angle or to congruent angles are congruent

Def. of complementary angles: <B and <C are complementary iff the sum of their measures is 90

Def. of supplementary angles: <A and <D are supplementary iff the sum of their measures is 180

Linear Pairs Postulate: If <1 and <2 form a linear pair, then <1 and <2 are supplementary

Def. of straight angles: If BA and BD are opposite rays, then <ABD is a straight angle and its measure is 180

Angle Bisector Theorem: If AB bisects <CAD, then m<CAB = 1/2m<CAD

Unit 2

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

Converse: If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel

Alternate Interior/Exterior Angles Theorem: If two parallel lines are cut by a transversal, then each pair of alternate interior/exterior angles is congruent

Alternate Interior/Exterior Angles Converse: If two lines are cut by a transversal and the alternate interior/exterior angles are congruent, then the lines are parallel

Same Side Interior/Exterior Angles Theorem: If two parallel lines are cut by a transversal, then each pair of same side interior/exterior angles is supplementary

Same Side Interior/Exterior Angles Converse: If two lines are cut by a transversal and the same side interior/exterior angles are supplementary, then the lines are parallel

Perpendicular Transversal Theorem: If line a is parallel to line b and line a is adjacent to line t, then line b is adjacent to line t

Perpendicular Transversal Converse: In a plane, if two lines are perpendicular to the same line, then they are parallel

Parallel Postulate: If given 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

Triangle Angle-Sum Theorem: The sum of the measures of the angles of a triangle is 180

Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measure of the two remote interior angles