# Geometry chapter 3 postulates and theorems

## 15 terms

### corresponding angles postulate

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

### parallel postulate

through a point outside a line, there is exactly one line parallel to the given line

### if <1 congruent <2 then m ll n

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

### slopes of parallel lines

two non-vertical lines are parallel if and only if their slopes are equal

### slopes of perpendicular lines

two non-vertical lines are perpendicular if and only if their slopes are opposite recipricols

### alternate interior angles theorem

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

### consecutive interior angles theorem

if two parallel lines are cut by a transversal then consecutive interior angles are supplementary

### alternate exterior angles theorem

if two parallel lines are cut by a transversal then alternate exterior angles are congruent

### perpendicular transversal theorem

if a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other as well

### if m<4+m<6 = 180 then m ll n

if two lines are cut by a transversal and consecutive interior angles are supplementary then the lines are parallel

### if m is perp. to p and n is perp. to p then m ll n

in a plane two lines perpendicular to the same line are parallel

### if <1 congruent <8 then m ll n

if two lines are cut by a transversal and alternate exterior angles are congruent then the lines are parallel

### * / ( point and line)

through a point outside a line there is exactly one line perpendicular to the given line

### m ll k and n ll k then m ll n

two lines parallel to a third line are parallel

### if <1+<2 = 90 and <1+<3 = 90 then <2 congruent to <3

if two angles are complementary to the same angle or congruent angles then the angles are congruent