Parallel Lines, Transversals,

& Special Angle

Pairs

When 2 lines intersectcrazy, wonderfulthings happen!

When 2 lines, rays or segments intersect, 4 angles are created.

1

2

3

4

Angles 1 & 4 are a linear pair = 180°Angles 1 & 2 are a linear pair = 180°Angles 2 & 3 are a linear pair = 180°Angles 3 & 4 are a linear pair = 180°

Angles 1 & 3 are VERTICAL ANGLES and are congruent.Angles 4 & 2 are VERTICAL ANGLES and are congruent.

Transversal

A line, ray, or segment that intersects

2 or moreCOPLANAR lines, rays, or segments.

Parallel lines

transversal

Non-Parallel lines

transversal

interior

INTERIOR –The space INSIDE the 2 lines

EXTERIOR -The space OUTSIDE the 2 lines

exterior

exterior

Special Angle Relationships

Interior Angles<3 & <6 are Alternate Interior angles<4 & <5 are Alternate Interior angles<3 & <5 are Same Side Interior angles<4 & <6 are Same Side Interior angles

1

4

2

65

7 8

3

Exterior Angles<1 & <8 are Alternate Exterior angles<2 & <7 are Alternate Exterior angles<1 & <7 are Same Side Exterior angles<2 & <8 are Same Side Exterior angles

Corresponding AnglesAngles that are in the same position on both

lines<1 & <5 are Corresponding angles<2 & <6 are Corresponding angles<3 & <7 are Corresponding angles<4 & <8 are Corresponding angles

Let’s PracticeNaming Angle Pairs$ $1 2

43

5 6

7 8

1. Name a pair of alternate interior angles

2. Name a pair of same side exterior angles

3. Name a pair of same side interior angles

4. Name a pair of alternate exterior angles

5. Name a linear pair6. Name a pair of vertical angles7. Name a pair of corresponding

angles8. Name another pair of

corresponding angles9. Name a linear pair10.Name a pair of vertical angles

Special Angle Measurement Relationships

WHEN THE LINES ARE PARALLEL

14

2

65

7 8

3

If the lines are not parallel, these measurement

relationships

DO NOT EXIST.

Check out the new notation. This extra set of arrows indicates parallel lines.

♥Alternate Interior Angles are CONGRUENT

♥Alternate Exterior Angles are CONGRUENT

♥Same Side Interior Angles are SUPPLEMENTARY

♥Same Side Exterior Angles are SUPPLEMENTARY

♥ Corresponding angles are CONGRUENT

Let’s look closer

When lines are not parallel, special angle pairs do not have

a measurement relationship.

When lines are parallel, measurement relationships

exist.

Either way, special angle pairs keep the same names.

1 2

3 4

5 6

871 2

43

5 67 8

Let’s Practice m<1=120°

Find all the remaining angle measures AND give the name of the special angle pair.

1

4

2

65

7 8

3

60°

60°

60°

60°

120°

120°

120°

120°

1 243

5 67 8

m<1=91°Find all the remaining angle measures

AND give the name of the special angle pair.

91°89°

89° 91°

WE DON’T KNOW!

Vocabulary

Parallel lines: Lines that are always equidistant from each other – they will never intersect. (2D or 3D)

Perpendicular lines: Lines that intersect at a 90◦ angle. (2D or 3D)

Skew lines: Lines that are not parallel but will never intersect. (3D only)

Use the diagram to name each of the following.

1. A pair of parallel planes

2. All lines that are parallel to

3. Four lines that are skew to

4. All lines that are parallel to plane QUV

5. A plane parallel to plane QUW

Identify all pairs of each type of angle in the diagram below right.

1. Corresponding angles2. Same-side interior angles3. Alternate interior angles4. Alternate exterior angles

Find the value of x and y. Then find the measure of each labeled angle.

♥ What kind of angles are these?

♥ What is their measurement relationship?

♥ How shall we set up the equation?

♥ Do it.

x + x – 26 = 1802x = 206x = 103

Are we done?

Angle measures are103 ◦ and 77◦

Another practice problem

Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.

40°

120°

Assignment

Practice 3.1 and 3.2