Parallel lines: two coplanar lines that never intersect.

Ex: AB and CD, AC and EG, FH and EG

Parallel planes: two planes that never intersect.

Ex:[] ABDC and [] EFHG, [] EACG and [] FBDH, [] ABFE and [] CDHG

Skew lines: two lines that have no relationship whatsoever.

Ex: AC and EF, GH and AE, BD and CG

A B

E F

([] means plane)

C D

G H

It is a line that intersects two other lines.

EX:

Corresponding: angles that lie in

the same side of the transversal.

EX: <1and<5, <4and<8, etc.

1 2

Alternate exterior: angles in the 3 4

opposite side of the transversal

but in the outside.

Ex: <1and<8 and <2and<7 5 6

7 8

Alternate interior: angles in the opposite

side of the transversal but in the interior.

Ex: <3and<6, <4and <5

Same-side interior: same side of the transversal in the interior.

Ex: <3and<5, <4and<6

Postulate: If two parallel lines are cut by a transversal, then the pairs of

corresponding angles are congruent.

Converse: if the pairs of corresponding angles are congruent, then two

parallel lines have to be cut by a transversal.

Corresponding angles:

<1and<5 1 2

<2and<6 3 4

<3and<7

<4and<85 6

7 8

Converse: If the pairs of Alternate Exterior angles are congruent, then

two parallel lines were cut by a transversal.

Alternate exterior angles:

<1and<8 1

2

<2and<7 3 4

5 6

7 8

Postulate: If two parallel lines are cut by a transversal, then the pairs of

Alternate Exterior angles are congruent.

Converse: If the pairs of Alternate Interior angles are congruent, then

two parallel lines were cut by a transversal.

Alternate exterior angles:

<3and<6 1 2

<4and<5 3 4

5 6

7 8

Postulate: If two parallel lines are cut by a transversal, then the pairs of

Alternate Interior angles are congruent.

Converse: If the pairs of Same-Side Interior angles are

Supplementary, then two parallel lines were cut by a transversal.

Alternate exterior angles:

<3and<5 1 2

<4and<6 3 4

5 6

7 8

Postulate: If two parallel lines are cut by a transversal, then the pairs of

Same-Side Interior angles are supplementary.

Theorem: If a line is perpendicular to one of the parallel lines, then it must be

perpendicular to the other line too.

Ex:

A _|_ B A _|_ C I _|_ G I _|_ Y M _|_ J M _|_ E

A G Y I

B

I J

C

E

We know that parallel lines never touch so if line A is parallel to line B and line B

is parallal to line C, then line A is parallel to line C.

In perpendicular lines this is not possible because if line A is perpendicular to line

B and B is perpendicular to line C then line A and line C mudt be parallel.

Ex: B B A B C

C

A C A

B

C A

Slope is the rise of a line over the run of that same line

(rise/run)

In many equations slope is represented by the lower-

case letter m.}

Formula: Y¹ –Y² (X,Y) (X,Y)

X¹- X²

1 no -1/3

slope 0

Parallel: All parallel lines have the

same slope as its complementing pair.

slopes: line1=1 line1= -

1/3

line2=1 line2= -

1/3

Perpendicular: All perpendicular lines

have the negative reciprocal slope of its

complementing pair.

slopes: line1= -1/3 line1=1/6

line2= 3/1 line2= -

Formula: Y=mX+b

You would use it when the slope and interceps are given.

Ex:

Y=1X+2 Y=1/2+1 Y=-2/3-2

Formula: Y-Y¹= m(X-X¹)

You would use it when points are given.

Ex:

Y-3=1(X+2) Y-0=1/2(X+3) Y+1=(X+0)