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Parallel Lines

Coplanar, equidistant, non-intersecting lines

Parallel Planes

Equidistant, non-intersecting planes

Skew Lines

Non-coplanar, non-intersecting lines

Transversal

Line that intersects two or more lines in a plane at different points

Interior Angles

Inside angles of two lines intersected by a transversal

Exterior Angles

Outside angles of two lines intersected by a transversal

Alternate Interior Angles

Inside angles of two lines intersected by a transversal and on opposite sides of the transversal (angles 3,6 and 4,5)

Alternate Exterior Angles

Outside angles of two lines intersected by a transversal and on opposite sides of the transversal (angles 2,7 and 1,8)

Consecutive Interior Angles

Inside angles of two lines intersected by a transversal and on the same side of the transversal (angles 4,6 and 3,5)

Corresponding Angles

Pair of angles formed by two lines and a transversal consisting of an interior angle and an exterior angle that have different vertices and that lie on the same side of the transversal (angles 2,6 and 1,5 and 4,8 and 3,7)

Corresponding Angles Postulate

Two parallel lines cut by a transversal create corresponding angles that are congruent.

Alternate Interior Angles Theorem

Two parallel linescut by a transversal create pairs of alternate interior angles that are congruent.

Consecutive Interior Angles Theorem

Two parallel lines cut by a transversal create pairs of consecutive interior angles that are supplementary.

Alternate Exterior Angles Theorem

Two parallel lines cut by a transversal create pairs alternate exterior angles that are congruent.

Perpendicular Transversal Theorem

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

Corresponding Angles Converse Postulate

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

Alternate Interior Angles Converse

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

Consecutive Interior Angles Converse

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

Alternate Exterior Angles Converse

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

Flow Proof

like a two column proof but the statements are connected by arrows to show how each statement comes from the ones before it

Vertical angles

if two angles sides form two pairs of opposite rays

Linear pair

two adjacent angles whoes noncommon sides are opposite

Parallel Postulate

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

Perpendicular Postulate

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

Congruent angles

Angles that have the same measure

perpendicular lines

two lines that intersect to form a right angle

oblique lines

when two lines intersect and are not perpendicular

coincident lines

when the graphs of two lines are the same or coincidentally on top of one another

linear pair postulate

If two angles form a linear pair, then they are supplementary (sum to 180)

vertical angles theorem

vertical angles are congruent

slope

= (y₂-y₁) / (x₂-x₁) [rise over run]

slope of parallel lines

the slopes of Parallel lines are the same
m = m

slope of perpendicular lines

negative reciprocals (flip and change signs)
m --> -1/m

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