Two Parallel lines

Do not intersect and are coplanar

Two skew lines

do not intersect and are not coplanar

Transversal

line that intersects two or more coplanar lines at different points

Corresponding Angles

Corresponding positions and congruent

Alternate interior angles

They lie between 2 lines and on opposite sides and Congruent

Alternate Exterior

They lie outside the 2 lines and are on opposite sides and congruent

Consecutive interior

They lie between two lines and on the same side and supplementary

Transitive Property of Parallel Lines

if p≅q & q≅r, then p≅q

Parallel Postulate

If there is a line and point not on the line, then there is exactly 1 line through the point parallel to the given line

Perpendicular Postulate

If there is a line and point not on the line then there is exactly 1 line through the point perpendicular to the given line

Corresponding Angles Postulate

If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

Alt. Interior Angles Theorem

If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Alt. Exterior Angles Theorem

If 2 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

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

Alt. Interior Angles Converse

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

Alt. Exterior Angles Converse

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

Consecutive Interior Angles Converse

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

Slope

y₂-y₁/x₂ -x₁

Slope Intercept form

mx +b=y

Standard Form

Ax + By= C

Point Slope Form

y-y₁=m(x-x₁)

Steep slope reminder

The absolute value of the slope, pick the higher one

Shortest distance between any 2 parallel lines

lies a ⊥ distance

If 2 lines intersect to form a linear pair of ≅ angles

then the lines are ⊥ (linear pair)

If 2 lines are ⊥

then they intersect to form 4 right angles

If 2 sides of 2 acute adjacent angles are ⊥

then the angles are complementary

Perpendicular Transversal Theorem

If a transversal is ⊥ to one of 2 parallel lines, then it is ⊥ to the second line

Lines ⊥ to a Transversal Theorem

In a plane, if 2 lines are ⊥ to the same line then the lines are parallel to one another

Slope of Parallel lines

They have the same slope

Slope of ⊥ (perpendicular) lines

product of Slopes have to equal -1, reciprocal and reverse sign