GEOMETRY Chapter 3: 3-1: Parallel Lines and Transversals

GEOMETRYChapter 3: 3-1: Parallel Lines and Transversals

Do Now: • Quick Ponder:

• What are parallel lines? How can we tell if two lines are parallel?

• Review: • If you are tired in class, then you may fall asleep

• What is the inverse of this statement?

• What is the converse of this statement?

Definitions: • Parallel Lines: are coplanar lines that do not intersect.

• Notation:

• Picture: Arrows are used to indicate that lines are parallel.

Definitions (continued) • Skew Lines: Are lines that do not intersect and are not

coplanar.

• No Notation

• Picture:

Definitions (Continued) • Parallel Planes: are planes that do not intersect.

• Notation: None

• Picture:

Example 1: • Identify each of the following using the wedge of cheese

below.

• a) All segments parallel to JP

• b) A segment skew to KL

• c) A plane parallel to plane PQR

Example 1: Answers • Identify each of the following using the wedge of cheese

below.

• a) All segments parallel to JP

- KQ and LR• b) A segment skew to KL

- JP, PQ, PR • c) A plane parallel to plane PQR

- Plane JKL

Example 2: • In the figure, assume that the lines and planes that

appear to be parallel are parallel.

• Which segments are parallel to AB?

• Which segments are skew to CD? 

• What are two pairs of parallel planes?

• What are two segments parallel to plane BCGF?

Example 2: Answers • In the figure, assume that the lines and planes that

appear to be parallel are parallel.

• Which segments are parallel to AB?

- CD, EF • Which segments are skew to CD?

- BF, AE, EF, EH, FG

What are two pairs of parallel planes?

- Plane ABCD is parallel to Plane EFGH

- Plane ADHE is parallel to EFGC• What are two segments parallel to plane BCGF?

• AE and HD

Definition: • Transversal: A line that intersects two or more coplanar

lines at two different points.

• Notation: None

• Picture: t is a transversal

of lines l and m

Definitions: • Interior Angles: Angles that lie in the region between two

lines.

Here interior angles are:

Definitions: • Interior Angles: Angles that lie in the region between two

lines.

Here interior angles are:

<3, <4, <5, <6

Definitions: • Exterior Angles: Angles that lie in the region outside of two

lines.

Here exterior angles are:

Definitions: • Exterior Angles: Angles that lie in the region outside of two

lines.

Here exterior angles are:

<1, <2, <7, <8

Definitions: • Consecutive Interior Angles: Interior Angles that lie on the

same side of a transversal.

Here consecutive interior

angles are:

Definitions: • Consecutive Interior Angles: Interior Angles that lie on the

same side of a transversal.

Here consecutive interior

angles are:

<3 and <6

<4 and <5

Definitions: • Alternate Interior Angles: are nonadjacent interior angles

that lie on opposite sides of a transversal.

Alternate Interior Angles:

Definitions: • Alternate Interior Angles: are nonadjacent interior angles

that lie on opposite sides of a transversal.

Alternate Interior Angles:

<4 and <6

<5 and <3

Definitions: • Alternate Exterior Angles: are nonadjacent exterior angles

that lie on opposite sides of a transversal.

Alternate Exterior Angles:

Definitions: • Alternate Exterior Angles: are nonadjacent exterior angles

that lie on opposite sides of a transversal.

Alternate Exterior Angles:

<1 and <7

<2 and <8

Definitions: • Corresponding Angles: lie on the same side of a

transversal and on the same side of the two lines the transversal intersects.

Corresponding angles:

Definitions: • Corresponding Angles: lie on the same side of a

transversal and on the same side of the two lines the transversal intersects.

Corresponding angles:

<1 and <5

<4 and <8

<2 and <6

<3 and <7

Example 3:

Example 4:

Practice Problems• Try some on your own/in table groups. • As always if you are confused please don’t hesitate to ask

me questions.

Exit Ticket

Name an example of each:

1.Corresponding Angles2.Alternate Exterior Angles3.Consecutive Interior Angles4.Alternate Interior Angles