CHAPTER 3: PARALLEL LINES AND PLANES

Section 3-1: Definitions

PARALLEL LINES

Two lines that do not intersect are either parallel or skew.

Parallel lines are coplanar lines that do not intersect.

Lines m and n are parallel.

m

n

SKEW LINES

Skew lines are noncoplanar lines. Therefore, they are neither parallel nor intersecting.

j and k are skew lines.

j

k

PARALLEL PLANES

Parallel planes are planes that do not intersect.

Planes A and B do not intersect.

A

B

PARALLEL PLANES

• A line and a plane are parallel if they do not intersect.

THEOREM 3-1

Theorem 3-1:

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

m

n

DEFINITIONS1. Transversal: is a line that intersects two

or more coplanar lines in different points.2. Alternate Interior Angles: are two

nonadjacent interior angles on opposite sides of the transversal.

3. Same-side interior Angles: are two interior angles on the same side of the transversal.

4. Corresponding Angles: are two angles in corresponding positions relative to the two lines.

CLASSIFYING ANGLESInterior Angles: 3, 4, 5, 6

Exterior Angles: 1, 2, 7, 8

Alternate Interior Angles:

3 and 6, 4 and 5

Same-Side Interior Angles:

3 and 5, 4 and 6

Corresponding Angles:

1 and 5, 2 and 6, 3 and 7, 4 and 8

h

k

t

1 23 4

5 67 8

PRACTICEClassify each statement as true or false.

1. A transversal intersects only parallel lines.

False

2. Skew lines are not coplanar.

True

3. If two lines are coplanar, then they are parallel.

False

4. If two lines are parallel, then exactly one plane contains them.

True

If j, k, and l are coplanar, name the transversal(s).

5. l

6. j,k,l

7. none

l jk

l

j k

j

k

l

CLASSWORK/HOMEWORK

• CW: Pg. 75, Classroom Exercises 1-9, 10-18 even.

• HW: Pg. 76, Written Exercises 2-20 even