parallel lines with transversals

Parallel Lines and Transversals

A

B

DC

Parallel Lines and Transversals

What would you call two lines which do not intersect?

Parallel

A solid arrow placed on two lines of a diagram indicate the lines are parallel.

The symbol || is used to indicate parallel lines.

AB || CD

Parallel Lines and Transversals

A slash through the parallel symbol || indicates the lines are not parallel.

AB || CD

AD

B

C

Parallel Lines and Transversals

Transversal -A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel.

t

mkj

Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

Parallel Lines and Transversals

Identifying Angles -

t

kj

1

23

45

67

8

Exterior angles are on the exterior of the two lines cut by the transversal.

The exterior angles are:

<1, <7, <2, <8

Parallel Lines and Transversals

Identifying Angles -

t

kj

1

23

45

67

8

Interior angles are on the interior of the two lines cut by the transversal.

The interior angles are:

<3, <5, <4, <6

Parallel Lines and Transversals

Identifying Angles -

t

kj

1

23

45

67

8

Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal.Alternate interior angles are:

<3 & <6, <4 & <5

Parallel Lines and Transversals

Identifying Angles -

t

kj

1

23

45

67

8

Alternate exterior angles are on the exterior of the two lines and on opposite sides of the transversal.

Alternate exterior angles are:

<1 & <8, <2 & <7

Parallel Lines and Transversals

Identifying Angles -

t

kj

1

23

45

67

8

Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal.

Corresponding angles are:

<1 & <5, <3 & <7, <2 & <6, <4 & <8

2. < 2 and < 10 are alternate interior angles.

Parallel Lines and Transversals

∠

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

Determine if the statement is true or false. If false, correct the statement.

1. Line r is a transversal of lines p and q.

2. < 2 and < 10 are alternate interior angles.

Parallel Lines and Transversals

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

Determine if the statement is true or false. If false, correct the statement.

1. Line r is a transversal of lines p and q.

True – Line r intersects both lines in a plane.

False - The angles are corresponding angles on transversal p.

4. < 1 and < 15 are alternate exterior angles.

3. <3 and < 5 are alternate interior angles.

Parallel Lines and Transversals

∠

∠

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

Determine if the statement is true or false. If false, correct the statement.

∠

∠

4. < 1 and < 15 are alternate exterior angles.

3. < 3 and < 5 are alternate interior angles.

Parallel Lines and Transversals

∠

∠

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

Determine if the statement is true or false. If false, correct the statement.

False – The angles are vertical angles created by the intersection of q and r.∠

True - The angles are alternate exterior angles on transversal p.

∠

6. < 10 and < 11 are consecutive interior angles.

5. < 6 and < 12 are alternate interior angles.

Parallel Lines and Transversals

∠

∠

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

Determine if the statement is true or false. If false, correct the statement.

∠

∠

6. < 10 and < 11 are consecutive interior angles.

5. < 6 and < 12 are alternate interior angles.

Parallel Lines and Transversals

∠

∠

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

Determine if the statement is true or false. If false, correct the statement.

True – The angles are alternate interior angles on transversal q.

∠

True – The angles are consecutive interior angles on transversal s.

∠

Determine if the statement is true or false. If false, correct the statement. 7. < 3 and < 4 are alternate

exterior angles.

8. < 16 and < 14 are corresponding angles.

Parallel Lines and Transversals

∠

∠

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

∠

∠

Determine if the statement is true or false. If false, correct the statement. 7. < 3 and < 4 are alternate

exterior angles.

8. < 16 and < 14 are corresponding angles.

Parallel Lines and Transversals

∠

∠

Identifying Angles – Check for Understanding

1 2 3 4

5678

9 10 11 12

13141516

∠

∠

False– The angles are adjacent angles on transversal r.

True – The angles are corresponding angles on transversal s.