Parallel and Perpendicular Lines

Honors Geometry Unit 3

Parallel Lines

2 lines that are coplanar and do not intersect

Skew Lines

2 lines that do not intersect and are not coplanar

Parallel Postulate

If a point is not on a line then there exists one and only one line through that point, parallel to the line

Perpendicular Postulate

If a point is not on a line then there exists one and only one line through that point, perpendicular to the line

Transversal

A line is a transversal if it intersects 2 or more lines, all at different points

Corresponding Angles

Same side of transversal in same "location" on different lines (are NOT same angle)

Alternate Exterior Angles

Different side of transversal, "outside" the lines

Alternate Interior Angles

Different side of transversal, "between" the lines

Consecutive Interior Angles

Same side of transversal, "between" the lines

Consecutive Exterior Angles

Same side of transversal, "outside" the lines

Corresponding Angles Postulate

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

Consecutive Exterior Angles Theorem

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

Alternate Interior Angles Theorem

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

Alternate Exterior Angles Theorem

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

Consecutive Interior Angles Theorem

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

Corresponding Angles Converse Postulate

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

Alternate Interior Angles Converse Theorem

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

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

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

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

Consecutive Exterior Angles Converse Theorem

If a pair of consecutive exterior angles are supplementary, then the lines are parallel

Perpendicular Lines

Two lines are perpendicular if they form at least one right angle

Congruent Linear Pair Theorem

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

Adjacent Complementary Angles Theorem

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary

Perpendicular Transversal Theorem

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

Lines perpendicular to a Transversal Theorem

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

Slope of Parallel Lines Postulate

In a coordinate plane, two nonvertical lines are parallel if and only if they have the same slope - only two vertical lines are parallel

Slope of Perpendicular Lines Postulate

In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is -1 - horizontal lines are perpendicular to vertical lines

Vertical Angles

Two angles that share a vertex and whose sides form two pairs of opposite rays

Linear Pair

Two adjacent angles whose non-common sides form opposite rays