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Parallel lines
do not intersect and are coplanar
Skew lines
do not intersect and are not coplanar
Symbols for parallel lines
small triangles on the lines and || when used in a statement
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
Transversal
a line that intersects two or more coplanar lines at different points
Corresponding angles
two angles that are in the same position
Alternate exterior angles
two angles that are outside the two lines and opposite sides of the transversal
Alternate interior angles
inside the two lines and opposite sides of the transversal
Consecutive interior angles
inside the two lines and same side of the transversal
Corresponding Angles Postulate
when parallel lines are cut by a transversal, corresponding angles are congruent
Alternate Interior Angles Theorem
when parallel lines are cut by a transversal, alternate interior angles are congruent
Alternate Exterior Angles Theorem
when parallel lines are cut by a transversal, alternate exterior angles are congruent
Consecutive Interior Angles Theorem
when parallel lines are cut by a transversal, consecutive interior angles are supplementary
Corresponding Angles Converse
when corresponding angles are congruent, the lines are parallel
Alternate Interior Angles Converse
when alternate interior angles are congruent the lines are parallel
Alternate Exterior Angles Converse
when alternate exterior angles are congruent the lines are parallel
Consecutive Interior Angles Converse
when consecutive interior angles are supplementary the lines are parallel
Lines Perpendicular to a Transversal Theorem
in a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other
Note
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