Geometry
Lesson Notes 3.2
Date ________________
Objective: Use the properties of parallel lines to determine congruent angles.
Use algebra to find angle measures.
Postulate 3.1 Corresponding Angles Postulate: If two parallel lines are cut by a transversal,
then corresponding angles are congruent.
Abbreviation: If PLCT, then corr. s 
Example 1 (p 133): Determine Angle Measures
Remember notation for parallel lines!
1
2
3
4
If m1 is 74, find m5.
5
If m6 is 110, find m3.
6
7
8
Notice that the previous statement is a postulate, the following statements are theorems.
Theorem 3.1 Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal,
then alternate interior angles are congruent.
Abbreviation: If PLCT, then alt. int. s 
Practice:
If m3 = 100, find m8.
If m7 = 3x + 4 and m4 = 120 – x, find x and m4 and m3.
t
2
1
4
3
m
7
8
5
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l
6
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Theorem 3.2 Consecutive Interior Angles Theorem: If two parallel lines are cut by a
transversal,then consecutive interior angles are supplementary.
Abbreviation: If PLCT, then cons. int. s suppl.
Abbreviation: If PLCT, then s.s. int. s suppl.
Practice:
If m3 = 100, find m7.
If m8 = 3x + 4 and m4 = 120 – x, find x and m8 and m6.
t
l
2
1
4
3
m
7
8
5
6
Theorem 3.3 Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal,
then alternate exterior angles are congruent.
Abbreviation: If PLCT, then alt. ext. s 
Practice:
If m2 = 78, find m5 and m6.
If m1 is 36 less than three times m6, find m1 and m6.
Example 2: Standardized Test Practice: Using an Auxiliary Line
G
What is the measure of GHJ?
A
Strategize! We are in the chapter about
parallel lines cut by a transversal but that
situation doesn’t exist in this picture.
So … add something to the picture!
E
B
40
H
70
C
 HW: A2a pp 136-137 #14-31
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J
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Theorem 3.4 Perpendicular Transversal Theorem: In a plane, if a line is perpendicular to one
of two parallel lines, then it is also perpendicular to the other.
l
t
m
1
2
t
Example 3 (p 135): Using Angle Relationships to Find Values of Variables
a. Be careful with when there are
multiple sets of parallel lines
and multiple transversals.
p
q
1 2
8 7
Angles is the special pairs must
be formed by the same transversal
cutting a pair of parallel lines.
Do 2 and 11 have any
relationship?
3 4
6 5
9 10
16 15
10 and 11?
10 and 6?
11 12
14 13
6 and 12?
b.
p
Find x and y.
q
x + 15
4(y − 25)
2x − 11
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E
Theorems must be proved!
Prove the Alternate Interior Angles Theorem:
If two parallel lines are cut by a transversal, then alternate interior angles are
congruent.
t
 Given: l || m
 Prove: 3  8
 Think about it:

I don’t know anything yet about the relationship
between 3 and 8. But I do know 3  6
because they are corresponding angles. I also
know that 6  8 because they are vertical angles.
I have a plan!
 Statements
1. l || m
2. 3  6
3. 6  8
4. 3  8
l
2
1
4
3
m
7
8
5
6
Reasons
1. Given
2. If PLCT, corr. s 
3. Vert. s 
4. Trans. Prop. of  s
 HW: A2b pp 136-138 #32-37*, 40, 45 *requires system of equations
A2c pp 136-138 #14-25, 32, 34, 36, 37*, 40
A2d 3-2 Skills Practice / Practice
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