Transversal Proofs, Slope & Equations, Parallel & Skew Lines

Corresponding Angles Theorem

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

Parallel Lines Postulate

two nonvertical lines have the same slope iff (if and only if) they are parallel

Perpendicular Lines Postulate

two nonvertical lines are perpendicular iff (if and only if) the product of their slopes is -1

Def. of a Perpendicular Bisector

Any line, segment, or ray that is perpendicular to a segment at its midpoint

• Must be a segment bisector

• Must be perpendicular

Slope Intercept Form

y = mx + b

(x,y), m is the slope, b is the y intercept

Standard Form

Ax + By = C

Standard Form Rule: __ ≥ __

A ≥ 0

Standard Form Rule: A must be a ____ number

A must be a whole number

Standard Form Rule: B & C must be an ____

B & C must be an integer

Standard Form Rule: The ___ of A, B, & C = 1

The Greatest Common Factor of A, B, & C must equal 1

Slope Intercept Form: Slope is written as ___ over ____

Slope is written as rise (increase in y) over run (increase in x)

Corresponding Angles Converse

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

Alternate Interior Angles Converse

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

Alternate Exterior Angles Converse

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

Consecutive Interior Angles Converse

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

Transitive Property of Parallel Lines

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

Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line

Perpendicular Transversal Converse

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

Perpendicular Postulate

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

Parallel Postulate

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

Parallel Lines

Coplanar lines that do not intersect

Skew Lines

Lines that do not intersect and are not coplanar

Parallel Planes

Planes that do not intersect