Postulate 3-1

Corresponding Angles Postulate

Corresponding Angles Postulate

If a transversal intersects two parallel lines, then corresponding angles are congruent

Theorem 3-1

Alternate Interior Angles Theorem

Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent

Theorem 3-2

Same-Side Interior Angles Theorem

Same-Side Interior Angles Theorem

If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

Theorem 3-3

Alternate Exterior Angles Theorem

Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then alternate exterior angles are congruent

Postulate 3-2

Converse of the Corresponding Angles Postulate

Converse of the Corresponding Angles Postulate

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel

Theorem 3-4

Converse of the Alternate Interior Angles Theorem

Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel

Theorem 3-5

Converse of the Same-Side Interior Angles Theorem

Converse of the Same-Side Interior Angles Theorem

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel

Theorem 3-6

Converse of the Alternate Exterior Angles Theorem

Converse of the Alternate Exterior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel

Theorem 3-7

If two lines are parallel to the same line, then they are parallel to each other

Theorem 3-8

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

Theorem 3-9

Perpendicular Transversal Theorem

Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other

Postulate 3-3

Parallel Postulate

Parallel Postulate

Through a point not on a line, there is one and only one line parallel to the given line

Theorem 3-10

Triangle Angle-Sum Theorem

Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180

Theorem 3-11

Triangle Exterior Angle Theorem

Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles

Postulate 3-4

Perpendicular Postulate

Perpendicular Postulate

Through a point not on a line, there is one and only one line perpendicular to the given line.