3-1 Properties of 3-1 Properties of Parallel linesParallel lines

Two or more lines Two or more lines are parallel if and are parallel if and only if they are in only if they are in the same plane the same plane and they do not and they do not intersect. (intersect. (line w line w and r)and r)

lw

lr

lr || lw

Two figures that Two figures that have the exact have the exact same size and same size and shape shape (example: two (example: two angles that have the angles that have the same measurement same measurement are congruent)are congruent)

lw

lr

= 122 Degrees

= 122 Degrees

lr || lw

A line intersecting A line intersecting twotwo or or moremore coplanar lines. coplanar lines. ((lines r and w)lines r and w)

lr

lw

lr || lw

If two parallel lines If two parallel lines are cut by a are cut by a transversal, then ……transversal, then …… Corresponding Corresponding

anglesangles are are congruentcongruent, , Alternate Interior Alternate Interior

anglesangles are are congruentcongruent, , . . . . And . . . . . . . . And . . . .

Alternate Exterior Alternate Exterior anglesangles are are congruent.congruent.

Same-Side Interior Same-Side Interior Angles are Angles are supplementraysupplementray

lw

lr 4411

3322

55 6677 88

55

11

55

441

8

If two parallel lines are cut by a transversal, If two parallel lines are cut by a transversal, then then Corresponding anglesCorresponding angles are are congruentcongruent..

1

5

2

6

3

7

4

8

lr

lw

lr || lw

If two angles are If two angles are Vertical anglesVertical angles, , then they are also then they are also congruentcongruent. .

1

4

2

3

587

6lw

lr

lr || lw

If two parallel lines are cut by a transversal, If two parallel lines are cut by a transversal, then then Alternate Exterior anglesAlternate Exterior angles are are congruentcongruent..

1

8

2

7lw

lr

lr || lw

If two parallel lines are cut by a transversal, If two parallel lines are cut by a transversal, then then Alternate Interior anglesAlternate Interior angles are are congruentcongruent..

3

6

4

5lw

lr

lr || lw

Since angle 1 = 58 ˚angle 1 = 58 ˚ then angle 4 = 58 ˚angle 4 = 58 ˚ and since angle 5 = 58 ˚angle 5 = 58 ˚ then angle 8 = 58 ˚angle 8 = 58 ˚ because they are vertical anglesvertical angles, which are congruent to each other

If angle 1 = 58 ˚angle 1 = 58 ˚ then angle 5 = 58 ˚angle 5 = 58 ˚ because they are corresponding anglescorresponding angles, which are congruent to each other

lr

lw

lr || lw

2233 44

665577 88

58 ˚58 ˚

58 ˚58 ˚

58 58 ˚̊

58 58 ˚ ˚

58˚58˚

5858˚̊

lr

lw

lr || lw

2233 44

665577 88

58 ˚58 ˚

121222˚

122122˚̊

122 ˚122 ˚

12122 ˚2 ˚

If angle 1 = 58 ˚angle 1 = 58 ˚ then angle 2 = 122 ˚angle 2 = 122 ˚ because the two angles form a lineline,which is equal to 180 ˚

Since angle 3 = 122 ˚angle 3 = 122 ˚ then angle 6 = 122 ˚angle 6 = 122 ˚ because they are Alternate Alternate Interior anglesInterior angles, which are congruent to each other.

Since angle 2 = 122 ˚angle 2 = 122 ˚ then angle 7 = 122 ˚angle 7 = 122 ˚ because they are AlternateAlternate Exterior angles Exterior angles, which are congruent to each other.

Compass Clipart from Microsoft OfficeCompass Clipart from Microsoft Office All other animals – pictures created by All other animals – pictures created by

Michelle A. O’MalleyMichelle A. O’Malley Serra, Michael. Serra, Michael. Discovering Discovering

GeometryGeometry. Berkeley: Key Curriculum . Berkeley: Key Curriculum Press, 1997.Press, 1997.