Transcript Slide 1

3.2 Angles and Parallel Lines
Objectives
Use the properties of
parallel lines to determine
congruent angles

Use algebra to find
angle measures

Postulate 3.1
Corresponding s Postulate

If 2  lines are cut by a
transversal, then each
pair of corres. s is .
1
2
l
m

i.e. If l m, then 12.
Theorem 3.1
Alternate Interior s Theorem

If 2  lines are cut by a transversal, then
each pair of alternate interior s is .
l
1
2
m

i.e. If l m, then 12.
Theorem 3.2
Consecutive Interior s Theorem

If 2  lines are cut by a transversal, then
each pair of consecutive int. s is
supplementary.
l
1
m
2

i.e. If l m, then 1 & 2 are supplementary or m1 + m2 = 180°.
Theorem 3.3
Alternate Exterior s Theorem

If 2  lines are cut by a transversal, then
the pairs of alternate exterior s are .
l
m
1
2

i.e. If l m, then 12.
Theorem 3.7
 Transversal Theorem

If a transversal is  to one of 2  lines,
then it is  to the other.
t
l
m

1
2
i.e. If l m, & t  l, then t m.
Example 2:
1
125o
Find:
m1 =
m2 =
m3 =
m4 =
m5 =
m6 =
x=
55°
125°
55°
2
3
5
4
125°
55°
125°
40°
x+15o
6
Example 3:
What is the measure of RTV?
Example 3:
Alternate Interior Angles Theorem
Definition of congruent angles
Substitution
Example 3:
Alternate Interior Angles
Theorem
Definition of congruent
angles
Substitution
Angle Addition
Postulate
Answer: RTV = 125°
Example 4:
ALGEBRA If
and
find x and y.
Find x.
by the Corresponding Angles
Postulate.
Example 4:
Definition of congruent angles
Substitution
Subtract x from each side and
add 10 to each side.
Find y.
by the Alternate Exterior Angles
Theorem.
Definition of congruent angles
Substitution
Example 4:
Simplify.
Add 100 to each side.
Divide each side by 4.
Answer:
Your Turn:
and
ALGEBRA If
find x and y.
Answer:
Assignment

Geometry:
Pg. 136 – 138 #14 – 27, 32 – 35, 39

Pre-AP Geometry:
Pg. 136 – 138 #14 - 39