Chapter 3 Geometry

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