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Lesson 3-1
Properties of Parallel Lines
Lesson Objectives
1 Identify angles formed by two lines
and a transversal
2 Prove and use properties of parallel
lines
California Content Standards
GEOM 2.0, GEOM 4.0, GEOM 7.0
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Vocabulary and Key Concepts.
Postulate 3-1: Corresponding Angles Postulate
If a transversal intersects two parallel lines, then corresponding
angles are
.
1
2
/
m
Theorem 3-1: Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate interior
angles are
.
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t
a
b
t
4
3 2
1
5 6
Theorem 3-2: Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines, then same-side interior
angles are
.
m1 m2 Theorem 3-3: Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then alternate exterior
angles are
.
Theorem 3-4: Same-Side Exterior Angles Theorem
If a transversal intersects two parallel lines, then same-side exterior
angles are
.
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Geometry Lesson 3-1
49
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A transversal is
t
56
13
42
78
/
m
Alternate interior angles are
Same-side interior angles are
and
are
same-side interior angles.
Corresponding angles are
and
corresponding angles.
A two-column proof is a display that shows
column shows
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and
are
alternate interior angles.
The first
and the second column
Examples.
1 Applying Properties of Parallel Lines In the diagram of
Compare 2 and the angle vertical to 1. Classify the angles
as alternate interior angles, same-side interior angles, or
corresponding angles.
2
3
1
The angle vertical to 1 is between the runway segments.
2 is between the runway segments and on the opposite side of the
transversal runway. Because
are not
adjacent and lie between the lines on opposite sides of the transversal,
2 and the angle vertical to 1 are
50
Geometry Lesson 3-1
.
Daily Notetaking Guide
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Lafayette Regional Airport, the black segments are runways
and the gray areas are taxiways and terminal buildings.
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p
2 Finding Measures of Angles
In the diagram at right, ᐉm and pq. Find m1 and m2.
1 and the 42 angle are
Because ᐉm, m1 q
8 6
7
2 1
3
.
by the
4
5
.
42
/
m
Because 1 and 2 are adjacent angles that form a
straight angle, m1 m2 If you substitute
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.
for m1, the equation becomes
from each side to find m2 Subtract
.
/
a b c
In the diagram, ᐉm. Find the values of a, b, and c.
a
Theorem
c
Theorem
b
.
3 Using Algebra to Find Angle Measures
abc
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by the
40
65
m
Postulate
Substitution Property of Equality
b
Subtraction Property of Equality
Quick Check.
1. Use the diagram in Example 1. Classify 2 and 3 as alternate interior angles,
same-side interior angles, or corresponding angles.
2. Using the diagram in Example 2 find the measure of each angle. Justify each answer.
a. 3
b. 4
c. 5
d. 6
e. 7
f. 8
3. Find the values of x and y. Then find the measures of the four angles
in the trapezoid.
y°
2x°
(y 50)°
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Geometry Lesson 3-1
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