Chapter 3: Parallel and Perpendicular Lines

These flashcards cover definitions, theorems, and key concepts related to parallel and perpendicular lines, commonly found in geometry.

Parallel Lines

Lines that do not intersect and are coplanar.

Skew Lines

Lines that do not intersect and are not coplanar.

Transversal

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

Corresponding Angles

Two angles formed by two lines and a transversal that are in the same relative position at each intersection.

Alternate Interior Angles

Two angles that lie between two lines and on opposite sides of the transversal.

Alternate Exterior Angles

Two angles that lie outside the two lines and on opposite sides of the transversal.

Consecutive Interior Angles

Two angles that lie between the two lines and on the same side of the transversal.

Corresponding Angles Theorem (Theorem 3.1)

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

Alternate Interior Angles Theorem (Theorem 3.2)

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

Alternate Exterior Angles Theorem (Theorem 3.3)

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

Consecutive Interior Angles Theorem (Theorem 3.4)

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

Corresponding Angles Converse (Theorem 3.5)

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

Alternate Interior Angles Converse (Theorem 3.6)

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

Alternate Exterior Angles Converse (Theorem 3.7)

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

Consecutive Interior Angles Converse (Theorem 3.8)

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

Transitive Property of Parallel Lines (Theorem 3.9)

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