Honors Geometry Cheat Sheet

Line Postulate

There exists exactly one line through any two points.

Plane Postulate

There exists exactly one plane through any three 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 (Properties of Equality)

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.

Definition of complementary angles

<B and <C are complementary if and only if the sum of their measures is 90.

Definition of supplementary angles

<A and <D are supplementary if and only if the sum of their measures is 180.

Linear Pairs Postulate

If <1 and <2 form a linear pair, then <1 and <2 are supplementary.

Definition 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.

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.