Chapter 3: Postulates, Theorems, and Corollaries

Corresponding angle Postulate

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent

Alternate interior angle theorem

If 2 parallel lines are cut by a transversal, then the alternate interior angles are congruent

Same side interior angle theorem

If 2 parallel lines are cut by a transversal, then the same side interior angles are supplementary

Alternate exterior angle theorem

If 2 parallel lines are cut by a transversal, then the alternate exterior angles are congruent

Same side exterior angle theorem

If 2 parallel lines are cut by a transversal, then the same side exterior angles are supplementary

Perpendicular transversal theorem

If a transversal is perpendicular to 1 of 2 parallel lines then it is perpendicular to the other

Converse of the Corresponding angle Postulate

If 2 lines are cut by a transversal and the corresponding angles are congruent, the then lines are parallel

Converse of the Alternate interior angle theorem

If 2 line are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel

Converse of the same side interior angle theorem

If 2 line are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel

Converse of the alternate exterior angle theorem

If 2 line are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel

Converse of the same side exterior angle theorem

If 2 line are cut by a transversal and the same side exterior angles are supplementary, then the lines are parallel

Converse of the perpendicular transversal theorem

In a plane, 2 lines perpendicular to the same line, are parallel

Parallel postulate

Given a line and a point not on that line, there is exactly 1 line THROUGH THE POINT parallel to the given line

Perpendicular postulate

Given a line and a point not on that line, there is exactly 1 line THROUGH THE POINT perpendicular to the given line

Theorem 3-10 (parallel transitive)

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

Triangle exterior angle theorem

The measure of an exterior angle in a triangle is equal to the sum of the remote INTERIOR angles

Interior angle sum theorem

The sum of the measures of the interior angles of a CONVEX polygon is (n - 2)*180

Exterior angle sum theorem

The sum of the measures of the exterior angles of a polygon is 360 degrees

Triangle ANGLE SUM theorem

The sum of the measures of the angles of a triangle equals 180 degrees

Describe corollaries

A statement that follows readily after a theorem

3rd angle corollary (tri. <. + theo)

If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the 3rd angles are congruent

Corollary 2 (tri. <. + theo.)

Each angle of angle equiangular triangle has a measure of 60 degrees

Corollary 3 (tri. <. + theo.)

In a triangle, there can be AT MOST 1 right or 1 obtuse angle

Corollary 4 (tri. <. + theo.)

The acute angles of a right triangle are complementary