Types of Lines & Planes

Parallel Lines: 2 lines on the same plane that never intersect

They are written as: ↔️AB || ↔️CD

Parallel Planes: 2 planes that never intersect

They are written as: plane a || plane b

Skew Lines: 2 lines on different planes that never intersect

Angles Formed by a Transversal

Corresponding Angles: Same side, same position

Example: Angles 1 and 3

Alternate Interior Angles: Different sides, on the inside

Example: Angles 2 and 6

Alternate Exterior Angles: Different sides, on the outside

Example: Angles 1 and 5

Consecutive Interior Angles: Same side, on the inside

Example: Angles 7 and 6

Consecutive Exterior Angles: Same side, on the outside

Example: Angles 1 and 4

Classifying Slopes

Positive Slope: ↗️

Negative Slope: ↘️

Zero: ↔️

Undefined: ↕️

Slope Formulas

Using a Graph: rise/run = m

Using ordered pairs: y2-y1/x2-x1 = m

Transitive Property (TP)

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

If p||q and q||r, then p||r

Converses of Angle Theorems

Corresponding Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

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

Alternate Interior Angles Theorem: If a transversal cuts two parallel lines, then the pairs of alternate interior angles are congruent

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

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

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

Consecutive Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

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

Consecutive Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of consecutive exterior angles are supplementary

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