Angles formed by Transversal and Parallel Lines

March 9, 2011

Warm Up 3/12/12

72

-4

1. Estimate to the nearest tenth: 70

2. Find - 169

3. Simplify and subtract: 5 8 3 32

4. Find n: 8 8

5. Write in standard form: 9.7 10

n

Warm Up 3/9/12

1. Simplify: 5 3 36 4 7

2. Solve for m: 2 5 5 3

3. Solve for x: 4 12

4. Multiply and simplify: 6 12 6 8

4 25. Simplify: 2 4

m m

x

Parallel Lines are…

…..coplanar lines that do not intersect.m

n

Skew lines are non-coplanar, non-intersecting lines.

m || n

p

q

The Transversal

Any line that intersects two or more coplanar lines.

r

s

t

The Transversal

When lines intersect, angles are formed in several locations.

r

s

t123 4

5678

When parallel lines are cut by a transversal…

Determine the two sets of angles that are congruent.

1, 4, 5, 8

2, 3, 6, 7

r

s

t

1 2

3 4

5 6

7 8

When parallel lines are cut by a transversal…

Angle pair relationships are formed.

Some angle pairs are congruent and other angle pairs are supplementary.

r

s

t

1 2

3 4

5 6

7 8

When parallel lines are cut by a transversal…

Congruent angles have the same measure.

r

s

t

1 2

3 4

5 6

7 8

2 3

When parallel lines are cut by a transversal…

• Supplementary Angles are angles that have a sum of 180 degrees.

r

s

t

1 2

3 4

5 6

7 82 8 180

When parallel lines are cut by a transversal…

Certain angles are given "names" that describe "where" the angles are located in relation to the lines.

r

s

t

1 2

3 4

5 6

7 8

When parallel lines are cut by a transversal…

r

s

t

1 2

3 4

5 6

7 8

INTERIOR

When parallel lines are cut by a transversal…

r

s

t

1 2

3 4

5 6

7 8

EXTERIOR

EXTERIOR

Corresponding Angles Corresponding

angles are congruent angles

on the same side of the transversal.

r

s

t

1

5 1 5

Corresponding Angles.r

s

t

2

6

2 6

Corresponding Angles

r

s

t

3

7

3 7

Corresponding Angles r

s

t

4

8

4 8

Alternate Interior Angles Alternate Interior

angles are congruent angles

on opposite sides of the transversal and inside the parallel

lines.

r

s

t

3

6

3 6

Alternate Interior Angles r

s

t

4

5

4 5

Alternate Exterior Angles Alternate Exterior

angles are congruent angles

on opposite sides of the transversal and outside the parallel

lines.

r

s

t

2

7 2 7

Alternate Exterior Angles r

s

t

1

8

1 8

Same Side Interior Same side interior

angles are supplementary

angles on the same side of the

transversal and inside the parallel

lines.

r

s

t

4

6

4 6 180

Same Side Interior r

s

t

3

5

3 5 180

Same Side Exterior Same side exterior

angles are supplementary

angles on the same side of the

transversal and outside the parallel

lines.

r

s

t

2

8 2 8 180

Same Side Exterior r

s

t

1

7

1 + 7 = 180

Vertical Angles

Vertical angles are congruent angles

located diagonally opposite each other.

r

s

t

1 2

3 4

5 6

7 8

1 4

Vertical Angles

r

s

t

2

3 2 3

Vertical Angles

r

s

t

5

8

5 8

Vertical Angles

r

s

t

6

7

6 7

2.

1.3. 4.

5. 6.7. 8.

Angle 2 measures 110°. What other angles have the same measure?

2.

1.3. 4.

5. 6.7. 8.

Answer: 2, 3, 6, 7

2.

1.3. 4.

5. 6.7. 8.

What is the measure of ?

1, 4, 5, 8

2.

1.3. 4.

5. 6.7. 8.

What is the measure of ?

1, 4, 5, 8

70Answer:

9) Lines l and m are parallel.l||m

Find the missing angles.

42°

l

m

4

5

8

23

6

7

9) Lines l and m are parallel.l||m

Find the missing angles.

42°

l

m

42°

42°

42°

138°138°

138°

138°

10) Lines l and m are parallel.l||m

Find the missing angles.

81°

l

m

4

5

8

23

6

7

10) Lines l and m are parallel.l||m

Find the missing angles.

81°

l

m

81°

81°

81°

99°99°

99°

99°

In the diagram below, j ║ k. What is m 1?

120°

j k

1

Solution

1. m 1 + 120° = 180°

2. m 1 = 60°

Find the value for x

125°

4(x + 15)°

1. m4 = 125°2. m4 +(x+15)°=180°3. 125°+(x+15)°= 180°4. x = 40

Solution