Section 2.2
The Postulates You Must Know
(Postulates are principles that are accepted to be true w/o proof)

Postulate 2-1: Through any two points, there is exactly one line

Postulate 2-2: Through any three points not on the same line, there is exactly one plane

Postulate2-3: A line contains at least two points

Postulate 2-4: A plane contains at least three points not on the same line

Postulate 2-5: If two points lie in a plane, then the entire line containing those two points
lies in that plane

Postulate 2-6: If two planes intersect, then their intersection is a line
Section 2.6
Verifying Angle Relationships

Thm 2-2 (Supplement Theorem): If two angles form a linear pair, then they are
supplementary angles

Thm 2-3: Congruence of angles is reflexive, symmetric, and transitive.

Thm 2-4: Angles supplementary to the same angle or to congruent angles are congruent.

Thm 2-5: Angles complementary to the same angle or to congruent angles are congruent.

Thm 2-6: All right angles are congruent.

Thm 2-7: Vertical angles are congruent

Thm 2-8: Perpendicular lines intersect to form four right angles
Section 3.1
Parallel lines and Transversals

Definition of Skew Lines: Two lines are skew if they do not intersect and are not in the
same plane
Section 3.2
Angles and Parallel Lines

Postulate 3-1 (Corresponding Angles Postulate): If two parallel lines are cut by a
transversal, then each pair of corresponding angles is congruent.

Thm 3-1 (Alternate Interior Angles Theorem): If two parallel lines are cut by a
transversal, then each pair of alternate interior angles is congruent.

Thm 3-2 (Consecutive Interior Angles Theorem): If two parallel lines are cut by a
transversal, then each pair of consecutive interior angles is supplementary.

Thm 3-3 (Alternate Exterior Angles Theorem): If two parallel lines are cut by a
transversal, then each pair of alternate exterior angles is congruent.

Thm 3-4 (Perpendicular Transversal Theorem): In a plane, if a line is perpendicular to
one of two parallel lines, then it is perpendicular to the other.
Section 3.3
Slopes of Lines

Postulate 3-2: Two nonvertical lines have the same slope if and only if they are parallel

Postulate 3-3: Two nonvertical lines are perpendicular if and only if the product of their
slopes is -1.
Section 3.4
Proving Lines Parallel

Postulate 3-4: If two lines in a plane are cut by a transversal so that the corresponding
angles are congruent, then the lines are parallel.

Postulate 3-5 (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.

Thm 3-5: If two lines in a plane are cut by a transversal so that a pair of alternate exterior
angles are congruent, then the two lines are parallel.

Thm 3-6: If two lines in a plane are cut by a transversal so that a pair of consecutive
interior angles is supplementary, then the lines are parallel.

Thm 3-7: If two lines in a plane are cut by a transversal so that a pair of alternate interior
angles is congruent, then the lines are parallel.

Thm 3-8: In a plane, if two lines are perpendicular to the same line, then they are parallel
Section 4.2
Measuring Angles in Triangles

Thm 4-1 (Angle Sum Theorem): The sum of the measures of the angles of a triangle is
180.

Thm 4-2 (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.

Thm 4-3 (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

Corollary 4-1: The acute angles of a right triangle are complementary

Corollary 4-2: There can be at most one right or obtuse angle in a triangle
Section 4.6
Analyzing Isosceles Triangles

Thm 4-6 (Isosceles Triangle Theorem): If two sides of a triangle are congruent, then the
angles opposite those sides are congruent.

Thm 4-7: If two angles of a triangle are congruent, then the sides opposite those angles
are congruent.

Corollary 4-3: A triangle is equilateral if and only if it is equiangular.

Corollary 4-4: Each angle of an equilateral triangle measures 60 degree.