# chapter 3

## 21 terms

### parallel lines

they do not intersect and are coplanar

### skew lines

do not intersect and are not coplanar

### parallel planes

two planes that do not intersect

### 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

is a line that intersects two or more coplanar lines at different points

### corresponding angles

if they have corresponding positions. if two angles are above the lines and to the right of the transversal

### alternate interior angles

if they lie between the two lines and on opposite sides of the transversal

### alternate exterior angles

if they lie outside the two lines and on opposite sides of the transversal

### consecutive interior angles

if they lie between the two lines and on the same side of the transversal

### corresponding angles postulate

if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

### alternate interior angles theorem

if two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent

### alternate exterior angles theorem

if two 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 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

### alternate interior angles converse

if two lines are cut by a transversal so the alternate interior angles are congruent then the lines are parallel

### alternate 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

### slopes of parallel lines

in a coordinate plane two nonvertical lines are parallel if and only if they have the same slope. any two vertical lines are parallel

### slopes of perpendicular lines

in a coordinate plane two nonvertical lines are perpendicular if an only if the product of their slopes is -1. Horizontal lines are perpendicular to vertical lines.