Chapter 2

Parallel lines

Coplanar lines that don’t intersect.

Skew lines

Noncoplanar lines that don’t intersect.

Parallel planes

Planes that don’t intersect.

Transversal

A line that intersects 2 or more coplanar lines at 2 different points.

Corresponding angles

Angles that lie on the same side of the transversal and on the same side of 2 lines.

Alternate exterior angles

Nonadjacent exterior angles that lie on opposite sides of a transversal.

Alternate interior angles

Nonadjacent interior angles that lie on opposite sides of a transversal.

Consecutive interior angles

Interior angles that lie on the same side of the transversal.

Corresponding Angle Postulate

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

Alternate Interior Angles Theorem

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

Consecutive Interior Angle Theorem

If 2 lines cut by a transversal are parallel, the consecutive interior angles are supplementary.

Alternate Exterior Angles Theorem

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

Perpendicular Transversal Theorem

If 2 lines cut by a transversal are parallel and the transversal is perpendicular to one of the parallel lines, then it must also be perpendicular to the other line.

Converse of Corresponding Angle Postulate

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

Consecutive Interior Angle Theorem Converse

If 2 lines are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the lines are parallel.

Alternate Interior Angle Theorem Converse

If 2 lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

Alternate Exterior Angles Theorem Converse

If 2 lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

Perpendicular Theorem Converse

If 2 lines are perpendicular to the same transversal, then the lines are parallel.

Parallel lines

Coplanar lines that don intersect

Skew lines

Noncoplanar lines that don intersect

Parallel planes

Planes that don intersect

Transversal

A line that intersects 2 or more coplanar lines at 2 different points (Can be at intersection points)

Corresponding angles

Angles that lie on the same side of the transversal and on the same side of 2 lines.

Alternate exterior angles

Nonadjacent exterior angles that lie on opposite sides of a transversal.

Alternate interior angles

Nonadjacent interior angles that lie on opposite sides of a transversal

Consecutive Interior Angles

Interior angles that lie on the same side of the transversal

Corresponding Angle Postulate

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

Alternate Interior Angles Theorem

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

Consecutive Interior Angle Theorem

If 2 lines cut by a transversal are parallel, the consecutive interior angles are supplementary.

Alternate Exterior Angles Theorem

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

Perpendicular Transversal Theorem

If 2 lines cut by a transversal are parallel and the transversal is perpendicular to one of the parallel lines, then it must also be perpendicular to the other line.

Converse of Corresponding Angle Postulate

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

Consecutive Interior Angle Theorem Converse

If 2 lines are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the lines are parallel.

Alternate Interior Angle Theorem Converse

If 2 lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

Alternate Exterior Angles Theorem Converse

If 2 lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

Perpendicular Theorem Converse

If 2 lines are perpendicular to the same transversal, then the lines are parallel.