Geometry

3.1 Lines and Transversals

Parallel Lines // Lines

Coplanar lines that do not intersect

j // k

j k

Skew Lines

Noncoplanar lines that do not intersect

line g is skew to line h g and h are skew lines

g

h

// and Skew Lines

What are some // lines in the diagram?

What are some skew lines in the diagram?

E A

B

C

DH

G

F

Segments and rays…

…contained in // lines are also parallel.

. B

. A . C

. D

AB // CD AB // CD

Are segments QP and RS parallel? They do not intersect!

But they are parts of lines PQ and RS, which are not parallel..

Thus, the answer is no!

Q

P

R S

// Planes…do not intersect

What are some parallel planes in the diagram?

Example: Plane ABCD // Plane EFGH

E A

B

C

DH

G

F

A line and a plane are // if they do not intersect!

Examples?

Example: Plane ABCD // EF

E A

B

C

DH

G

F

Theorem

If two parallel planes are cut by a third plane, then the lines of intersection are parallel.

j

k

j // k

Transversal

A line that intersects two or more coplanar lines in different points.

t

t is a transversal

The lines do not need to be parallel to have a transversal !

Interior Angles and Exterior Angles Exterior angles 1, 2, 7, and 8. Interior angles 3, 4, 5, and 6.

t1 2

7 8

3 4

5 6

The lines do not need to be parallel for this to be true!

Alternate Interior Angles(Alt. Int <‘s) Two nonadjacent interior angles on opposite

sides of the transversal. What are the two pairs of Alt. Int. <‘s?

t1 2

7 8

3 4

5 6

<3 and <6 <4 and <5

The lines do not need to be parallel for this to be true!

Same Side Interior Angles(S.S. Int <‘s) Two interior angles on the same side of the

transversal. What are the two pairs of S.S. Int. <‘s?

t1 2

7 8

3 4

5 6

<3 and <5 <4 and <6

The lines do not need to be parallel for this to be true!

Corresponding Angles(Corr. <‘s) Two angles in corresponding positions

relative to the two lines. What are the four pairs of Corr. <‘s?

t1 2

7 8

3 4

5 6

<1 and <5 <2 and <6

<3 and <7 <4 and <8

The lines do not need to be parallel for this to be true!

Finding a transversal Trace each < identified. The line you touch twice is the transversal. Name the two lines and the transversal between angles…It helps to

draw an isolated picture

2

34

6

5

71

8A

B

C

D Angles 1 and 5

Transversal AE

E

Angles 2 and 6

Transversal BCF

Angles 4 and 7Transversal EF

Sometimes, Always, or Never? When there is a transversal of 2 lines, the 3

lines are _________ coplanar. Answer: Always 2 Lines that are not coplanar __________

intersect. Answer: Never 2 Planes // to the same line are _________ //

to each other. Answer: Sometimes

Review Sheet

Please open your books to page 76

#4, 6, 12, 18, 24, 26, 34, 384) Alt. Int <‘s6) Corr. <‘s8) Lines PS, QR, and transversal SQ12) Corr. <‘s18) Corr. <‘s are congruent24) GH, ED, KJ26) CDJI and GHIJKL34) Sometimes38) Sometimes

HW

P. 76 – 77, #1-41 odd, skip 19 and 21 Self Test P. 65 Odds

Vocab Quiz tomorrow, Chapter 2 Test Friday Ch. Review Today