Geometry 3.1-3.4

parallel lines

coplanar lines that never intersect
(symbol is ll)

skew lines

noncoplanar lines that never intersect

parallel planes

planes that never intersect

alternate interior angles

two angles inside the two lines but on opposite sides of the transversal
(AIA - makes a Z or N)

alternate exterior angles

two angles on opposite sides of the transversal and outside of the two lines
(AEA)

consecutive interior angles

two angles on the same sid of the trasversal and inside both lines
(CIA - make goal posts - aka same side interior angles)

corresponding angles

two angles in the same position relative to the two lines and the transversal

parallel postulate

If there is a line and a point not on a line, then there is exactly one parallel through that point to the given line.

perpendicular postulate

If there is a line and a point not on the line, then there is exactly one perpendicular through that point to the given line.

corresponding angles postulate

if 2 parallel lines are cut by a transversal then corresponding angles are congruent
(corr. ang. post.)

alternate interior angles theorem

if 2 parallel lines are cut by a transversal than alternate interior angles are congruent
(AIA theorem)

consecutive interior angles theorem

if parallel lines are cut by a transversal the consecutive interior angles are supplementary
(CIA theorem)

alternate exterior angles theorem

if parallel lines are cut by a transversal the alternate exterior angles are congruent
(AEA theorem)

6 methods to prove lines are parallel

1. show corr. < are congruent (converse of corr. < post.)
2. show cons. int. < are supp. (conv. CIA theorem)
3. show alt. ext. < are congruent (conv. of AEA theorem)
4. show alt. int. < are congruent (conv. of AEA theorem)
5. show slopes are congruent
6. show their coplanar lines can never intersect

slope intercept form

y=mx+b

standard form

Ax+By=C

point slope form

y-y1=m(x-x1)
(y1 and x1 are the points the line intersects through)