Download PPT 2.6 Special Angles on Parallel Lines

Warm-Up
2.6 Parallel Line Angles Objective
Explore relationships of the angles formed by a
transversal cutting parallel lines.
HW: p. 141 #1, 3-6, 9-10 (DUE Tuesday 9/29)
Investigation “Which angles are
congruent?”

Step 1) Using a ruler, draw a pair of parallel lines on your
paper.

Step 2) Draw a line that intersects both parallel lines (a
transversal).

Step 3) Label the Angles 1-8
1
3
5
7
6
8
2
4

Step 4) Place the patty paper over angles 1-4
and trace the intersecting lines and the four
angles.
1
3
2
4

Step 5) Slide the patty paper down to angles
5-8. What do you notice?
1
3
2
4
Transveral
Special Angles on Parallel Lines
Keyword
Conjecture
Sketch
Corresponding
Angles (CA)
congruent
Corresponding Angles are ___________.
Alternate Interior
Angles (AIA)
congruent
Alternate Interior angles are __________.
1
8
1
3 4
6
5
7
Alternate Exterior
Angles (AEA)
3 4
6
5
7
8
congruent
Alternate Exterior angles are _________.
1
3 4
6
5
7
8
2
2
2
Special Angles on Parallel Lines
Keyword
Conjecture
Consecutive Interior
Angles
Same Side Interior Angles
are _______________.
supplementary
Consecutive Exterior
Angles
Same side exterior angles
supplementary
are ______________.
Sketch
1
8
1
7
2
3 4
6
5
Parallel lines
Conjecture
3 4
6
5
7
2
8
If two parallel lines are cut by a transversal, then
corresponding angles are ____________,
congruent alternate
interior angles are ______________,
and alternate
congruent
congruent
exterior angles are ________________.
Special Angles on Parallel Lines
Converse of 
Parallel
Lines
Conjecture
If 2 lines are cut by a transversal to form pairs of
congruent Corresponding Angles, congruent
Alternate Interior Angles, congruent Alternate
Exterior Angles, supplementary Consecutive
interior angles, or supplementary exterior angles,
parallel
then the lines are ________________.
BASICALLY:
IF ALL THE ANGLS ARE CONGRUENT, THEN
THE LINES ARE PARALLEL
Practice Time!
1) Find the missing angle.
?°
36°
1) Find the missing angle.
?°
36°
90 ° – 36 = 54°
2) Find the missing angle.
?°
64°
2) Find the missing angle.
?°
64°
90 ° – 64° = 26°
3) Solve for x.
2x°
3x°
3) Solve for x.
2x°
3x°
3x° + 2x° = 90°
5x = 90
x =18
4) Solve for x.
x + 25
2x + 5
4) Solve for x.
x + 25
2x + 5
(2x + 5) + (x + 25) = 90
3x + 30 = 90
3x = 60
x = 20
5) Find the missing angle.
?°
168°
5) Find the missing angle.
?°
180° – 168° = 12°
168°
6) Find the missing angle.
58°
?°
6) Find the missing angle.
58°
180° – 58° = 122°
?°
7) Solve for x.
4x
5x
7) Solve for x.
4x
4x + 5x = 180
9x = 180
x = 20
5x
8) Solve for x.
2x + 10
3x + 20
8) Solve for x.
2x + 10
3x + 20
(2x + 10) + (3x + 20) = 180
5x + 30 = 180
5x = 150
x = 30
9) Lines l and m are parallel.
l||m
Find the missing angles.
42°
a°
c°
b°
d°
e°
g°
f°
l
m
9) Lines l and m are parallel.
l||m
Find the missing angles.
42°
138°
138°
42°
42°
138°
138°
42°
l
m
10) Lines l and m are parallel.
l||m
Find the missing angles.
81°
a°
c°
b°
d°
e°
g°
f°
l
m
10) Lines l and m are parallel.
l||m
Find the missing angles.
81°
99°
99°
81°
81°
99°
99°
81°
l
m
x + (2x + 45) = 180
3x + 45 = 180
3x = 135
x = 45
11) Find the missing angles.
70 °
70 °
b°
Hint: The 3 angles in a
triangle sum to 180°.
d°
65 °
11) Find the missing angles.
70 °
70 °
40°
Hint: The 3 angles in a
triangle sum to 180°.
75 °
65 °
12) Find the missing angles.
45 °
50 °
b°
Hint: The 3 angles in a
triangle sum to 180°.
d°
75 °
12) Find the missing angles.
45 °
50 °
85°
Hint: The 3 angles in a
triangle sum to 180°.
20°
75 °
In the figure a || b.
13. Name the angles congruent to 3.
1, 5, 7
14. Name all the angles supplementary to 6.
1, 3, 5, 7
15. If m1 = 105° what is m3?
105°
16. If m5 = 120° what is m2?
60°
The End
Exit Ticket 2.6
s
k
i
d
c
j
g
64
a
b
h
108
f
e
75
m
p
79
n
169
q
t
61