Unit 3

Parallel Lines

Coplanar lines that never intersect, no matter how far they extend.

Skew Lines

Non-coplanar lines that are not parallel and never intersect (they exist in different 3D planes).

Transversal

A line that intersects two or more coplanar lines at distinct points.

Interior Angles

The four angles that lie in the region between the two lines intersected by the transversal.

Exterior Angles

The four angles that lie in the region outside the two lines intersected by the transversal.

Consecutive Interior Angles

A pair of interior angles that lie on the same side of the transversal.

Consecutive Exterior Angles

A pair of exterior angles that lie on the same side of the transversal.

Alternate Interior Angles

A pair of nonadjacent interior angles that lie on opposite sides of the transversal.

Alternate Exterior Angles

A pair of nonadjacent exterior angles that lie on opposite sides of the transversal.

Corresponding Angles

A pair of nonadjacent angles (one interior, one exterior) that lie on the same side of the transversal in matching relative positions.

Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then each pair of corresponding angles is exactly congruent.

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

Alternate Exterior Angles Theorem

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

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary (they add up to 180°).

Consecutive Exterior Angles Theorem

If two parallel lines are cut by a transversal, then each pair of consecutive exterior angles is supplementary (they add up to 180°).

Converse

A statement formed by swapping the hypothesis and conclusion of a conditional statement. If the original is $p \rightarrow q$, the converse is $q \rightarrow p$.

Converse of the Corresponding Angles Postulate

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

Parallel Postulate

Given a line and a point not on that line, there exists exactly one line through that point that is parallel to the given line.

Converse of the Alternate Interior Angles Theorem

If two lines are cut by a transversal so that alternate interior angles are congruent, then the two lines must be parallel.

Converse of the Alternate Exterior Angles Theorem

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the two lines must be parallel.

Converse of the Consecutive Interior Angles Theorem

If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the two lines must be parallel.

Converse of the Consecutive Exterior Angles Theorem

If two lines are cut by a transversal so that consecutive exterior angles are supplementary, then the two lines must be parallel.

Perpendicular Transversal Converse

In a flat plane, if two separate lines are both perpendicular to the exact same transversal line, then those two lines are parallel to each other.