Parallel lines transversals
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Parallel Lines & Transversals. Notes 12 – Section 3.1. Essential Learnings. Students will understand and be able to identify the relationship between two lines or two planes. Students will be able to identify angle pairs formed by parallel lines and transversals. Vocabulary.

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Parallel Lines & Transversals

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Parallel lines transversals

Parallel Lines & Transversals

Notes 12 – Section 3.1


Essential learnings

Essential Learnings

  • Students will understand and be able to identify the relationship between two lines or two planes.

  • Students will be able to identify angle pairs formed by parallel lines and transversals.


Vocabulary

Vocabulary

  • Parallel lines – coplanar lines that do not intersect.

  • Skew lines – lines that do not intersect and are not coplanar.

  • Parallel planes – planes that do not intersect


Vocabulary1

Vocabulary

  • Transversal – a line that intersects two or more coplanar lines at two different points.

1

2

3

4

5

6

7

8


Angle pair relationships

Angle Pair Relationships

  • Interior angles – lie inside the two lines cut by the transversal.

  • Exterior angles – lie outside the two lines cut by the transversal.

    InteriorExterior

1

2

3

4

3, 4,

5, 6

1, 2,

7, 8

5

6

7

8


Angle pair relationships1

Angle Pair Relationships

  • Consecutive interior angles – interior angles that lie on the same side of the transversal.

  • Corresponding angles – lie on the same side of the transversal and on the same side of the two lines that the transversal cuts.


Example 1

Example 1

Identify the following from the figure:

Consecutive interior angles

Corresponding angles

1

2

3 &5

4 &6

3

4

5

6

7

8

1 &5, 3 &7

2 &6 4 &8


Angle pair relationships2

Angle Pair Relationships

  • Alternate interior angles – angles that are nonadjacent interior angles that lie on opposite sides of the transversal.

  • Alternate exterior angles – angles that are nonadjacent exterior angles that lie on opposite sides of the transversal.


Example 2

Example 2

Identify the following from the figure:

Alternate interior angles

Alternate exterior angles

1

2

3 &6

4 &5

3

4

5

6

7

8

1 &8

2 &7


Example 3

Example 3

Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠1 and ∠8

∠4 and ∠7

∠2 and ∠6

∠4 and ∠5

1

2

3

4

5

7

6

8


Example 4

Example 4

Identify the transversal connecting each pair of angles in the figure then classify the relationship between the angles.

∠1 and ∠4

∠4 and ∠5

∠2 and ∠5

∠6 and ∠8

b

1

2

5

3

4

c

a

d

6

7

e

8

f


Example 5

Example 5

  • Describe the relationship between each pair of segments as parallel, skew, or intersecting.

    AB and CG

    DH and BF

    CD and AD

B

C

D

A

F

G

E

H


Assignment

Assignment

Pages 174-175: 22-44 even

USG 2 – Keep working on it!

Finish Mastery Assignment – Due Friday


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