Geometry: Parallel Lines, Special Angles, and Indirect Proof

Vocabulary flashcards covering parallel lines, special angle pairs, the parallel postulate, indirect proofs, and theorems for proving lines parallel.

Parallel Lines

Lines in the same plane that do not intersect.

Parallel Planes

Planes that do not intersect.

Point Parallel Postulate

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

Transversal

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

Corresponding Angles

Angles that lie in the same relative location at each intersection where a transversal cuts two lines.

Alternate Interior Angles

Angles that lie between the two lines on opposite sides of the transversal.

Alternate Exterior Angles

Angles that lie outside the two lines on opposite sides of the transversal.

Same Side Interior Angles

Angles that lie between the two lines on the same side of the transversal.

Same Side Exterior Angles

Angles that lie outside the two lines on the same side of the transversal.

Corresponding Angles Postulate

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

Alternate Interior Angles Theorem

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

Alternate Exterior Angles Theorem

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

Same Side Interior Angles Theorem

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

Same Side Exterior Angles Theorem

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

Point-Perpendicular Theorem

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Converse Corresponding Angles Theorem

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

Converse Alternate Interior Angles Theorem

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

Converse Alternate Exterior Angles Theorem

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

Converse Same Side Interior Angles Theorem

If two lines are cut by a transversal so that same side interior angles are supplementary, then the lines are parallel.

Converse Same Side Exterior Angles Theorem

If two lines are cut by a transversal so that same side exterior angles are supplementary, then the lines are parallel.

Three Parallel Line Theorem

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

Plane, Perpendicular, Parallel Theorem

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