Topic 2: Parallel and Perpendicular Lines

For Geometry Honors.

Parallel Lines

Coplanar lines that never intersect.

Parallel Planes

Planes that never intersect.

Skew Lines

Non-coplanar lines that never intersect.

Transversal

A line that intersects two or more lines.

Corresponding Angles

Angles on the same side of the transversal and in the same position, ≅ (congruent).

Alternate Interior Angles

Interior angles, non-adjacent, and on opposite sides of the transversal ≅ (congruent).

Alternate Exterior Angles

Exterior angles, non-adjacent, and on opposite sides of the transversal, ≅ (congruent).

Consecutive Interior Angles

Interior angles that are on the same side of the transversal, are 180° (supplementary).

Consecutive Exterior Angles

Exterior angles that are on the same side of the transversal, are 180° (supplementary).

Converse

A conditional statement that is created when the hypothesis and conclusion are reversed.

Corresponding Angles Converse

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

Alternate Interior Angles Converse

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

Alternate Exterior Angles Converse

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

Consecutive Interior Angles Converse

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

Consecutive Exterior Angles Converse

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

Transitive Property of Parallel Lines

If two lines are parallel to the same line, then they are parallel to each other (If p ‖ q and q ‖ r, then p ‖ r).