Geometry chapter 3 postulates and theorems

parallel lines theorem 3.8

2 lines that are parallel to the same line are parallel to each other

theorem 3.9-parallel lines

2 lines that are perpendicular to the same line are parallel to each other

Theorem 3.2 (Same-Side Interior Angles Theorem)

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

congruent supplement theorem

If two angles are supplementary to the same angle, then they are congruent

Theorem 3.7 - converse of alternate exterior angles theorem

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

Theorem 3.5 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 3.6- Converse of 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.

Corresponding Angles Postulate

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

Theorem 3.1 Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Exterior and interior angle of a triangle

The measure of each exterior angle of a triangle equals the sum of the measures of its 2 remote interior angles.

Congruent Complements Theorem

if two angles are complementary to the same angle, then they are congruent

Theorem 3.3 Alternate Exterior Angles Theorem

if two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent

vertical angles theorem

vertical angles are congruent

Perpendicular transversal theorem- 3.10

A line that is perpendicular to 1 of 2 parallel lines is also perpendicular to the other line.

Theorem 3.11- triangle angle-sum theorem

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

Parallel line postulate 3.2

Through a point not on a line, there is exactly one line parallel to the given line.