Download 3-2 - Ithaca Public Schools

Name_____________________________________ Class____________________________ Date________________
Lesson 3-2
Lesson Objectives
1 Use a transversal in proving lines
parallel
Proving Lines Parallel
NAEP 2005 Strand: Measurement
Topic: Measuring Physical Attributes
Local Standards: ____________________________________
Vocabulary and Key Concepts.
1
/
m
If two lines and a transversal form
2
If two lines and a transversal form
.
5 6
1 4
2
m
3
If 1 2,
/
then
.
Theorem 3-6: Converse of the Same-Side Interior Angles Theorem
If 2 and 4 are
If two lines and a transversal form
supplementary,
then
.
Theorem 3-7: Converse of the Alternate Exterior Angles Theorem
If 3 5,
If two lines and a transversal form
then
Theorem 3-8: Converse of the Same-Side Exterior Angles Theorem
If 3 and 6 are
If two lines and a transversal form
supplementary,
then
52
Geometry Lesson 3-2
.
.
Daily Notetaking Guide
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Theorem 3-5: Converse of the Alternate Interior Angles Theorem
All rights reserved.
Postulate 3-2: Converse of the Corresponding Angles Postulate
Name_____________________________________ Class____________________________ Date ________________
A flow proof uses
Reasons are written
Examples.
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1 Using Postulate 3-2
Use the diagram at the right. Which lines, if any, must be parallel
if 3 and 2 are supplementary? Justify your answer with
a theorem or postulate.
E
It is given that 3 and 2 are supplementary. The diagram
shows that
and
D1
are supplementary. Because
3
C
4K
2
supplements of the same angle are
(Congruent Supplements Theorem),
and
. Because
are congruent corresponding angles,
by the
Postulate.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
2 Using Algebra
Find the value of x for which m.
The labeled angles are
.
If m, the alternate interior angles are
and their measures are
66 equation
66 3x
3x
x
Daily Notetaking Guide
,
(14 3x)
/
(5x 66)
. Write and solve the
m
3x.
Add
Subtract
to each side.
from each side.
Divide each side by
.
Geometry Lesson 3-2
53
Name_____________________________________ Class____________________________ Date________________
Quick Check.
1. Use the diagram from Example 1. Which lines, if any, must be parallel if
3 4? Explain.
2. Find the value of x for which a b. Explain how you can check your answer.
a
62
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
All rights reserved.
b
(7x 8)
54
Geometry Lesson 3-2
Daily Notetaking Guide