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# Chapter Three

### Parallel Lines and Transversals

TermDefinition
parallel lines coplanar lines that do not intersect
parallel planes planes that do not intersect
skew lines lines that do not intersect and are not coplanar
transversal a line that intersects two or more coplanar lines at two different points
same side (consecutive) interior angles interior angles that lie on the same side of the transversal
alternate interior angles nonadjacent interior angles that line on opposite sides of the transversal
alternate exterior angles nonadjacent exterior angles that lie on opposite sides of the transversal
corresponding angles lie on the same side of the transversal and on the same side of the lines.
Corresponding Angles Postulate if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.
Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.
Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent.
Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
slope ratio of the change along the y-axis to the change along the x-axis between any two points on the line.
Four Different Types of Slope (positive slope, negative slope, zero slope, undefined slope)
rate of change how a quantity y changes in relationship to a quantity x.
Slope of Parallel Lines Postulate Two nonvertical lines have the same slope IFF they are parallel. Are vertical lines are parallel.
Slope of Perpendicular Lines Postulate Two nonvertical lines are perpendicular IFF the product of their slope is -1. Vertical and horizontal lines are perpendicular.
Slope-Intercept Form y=mx+b, where m is the slope of the line and b is the y intercept.
point-slope form y-y1=m(x-x1) where (x1,y1) is any point on the line and m is the slope of the line.
Horizontal Line The equation of a horizontal line is y=b where b is the y-intercept of the line.
Vertical Line The equation of a vertical line is x=a, where a is the x-intercept of the line.
Postulate 3.4: Converse of Corresponding Angles Postulate If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Postulate 3.5 Parallel Postulate If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.
Theorem 3.5 Alternate Exterior Angle Converse If two lines in a plane are cut by a transversal so that a pair of alterate exterior angles is congruent, then the two lines are parallel.
Theorem 3.6 Consecutive Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the lines are parallel.
Theorem 3.7: Alternate Interior Angles Converse If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the lines are parallel.
Theorem 3.8: Perpendicular Transversal Converse In a plane, if two lines are perpendicular to the same line, then they are parallell.
Distance between a point and a line The distance between a line and a point not on the line is the length of the segment perpendicular to the line from the point.
Postulate 3.6 Perpendicular Postulate If given a line and a point not on the line, then there exists exactly one line through the point that is perpendicular to the given line.
equidistant the distance between two lines measured along a perpendicular line to the lines is always the same.
Distance between Parallel Lines the distance betweeen 2 parallel lines is the perpendicular distance between one of the lines and any point on the other line.
Theorem 3.9 Two Lines Equidistant from a Third In a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other.
Created by: amgeometry