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transcript
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
t
123 4
56
78
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
72 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
2
3
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