Download 11/10 Notes - Converse Theorems

2-7
2-7 Flowchart
Flowchartand
andParagraph
ParagraphProofs
Proofs
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
Geometry
2-7 Flowchart and Paragraph Proofs
Warm Up
Complete each sentence.
1. If the measures of two angles are
? , then the
angles are congruent. equal
2. If two angles form a ? , then they are
supplementary. linear pair
3. If two angles are complementary to the same
angle, then the two angles are
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? . congruent
2-7 Flowchart and Paragraph Proofs
Objectives
Write flowchart and paragraph proofs.
Converse Postulates
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2-7 Flowchart and Paragraph Proofs
Vocabulary
flowchart proof
paragraph proof
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2-7 Flowchart and Paragraph Proofs
Note 37
A second style of proof is a flowchart proof, which
uses boxes and arrows to show the structure of the
proof.
The justification for each step is written below the
box.
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2-7 Flowchart and Paragraph Proofs
Example 1: Reading a Flowchart Proof
Given: 2 and 3 are comp.
1  3
Prove: 2 and 1 are comp.
Flowchart proof:
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2-7 Flowchart and Paragraph Proofs
Note 37 (cont.)
A paragraph proof is a style of proof that
presents the steps of the proof and their
matching reasons as sentences in a paragraph.
Although this style of proof is less formal than
a two-column proof, you still must include
every step.
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2-7 Flowchart and Paragraph Proofs
Example 3: Reading a Paragraph Proof
Given: m1 + m2 = m4
Prove: m3 + m1 + m2 = 180°
Paragraph Proof: It is given that
m1 + m2 = m4. 3 and 4 are
supplementary by the Linear Pair Theorem.
So m3 + m4 = 180° by definition. By
Substitution, m3 + m1 + m2 = 180°.
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2-7 Flowchart and Paragraph Proofs
Note 38
Holt Geometry
2-7 Flowchart and Paragraph Proofs
Example 1B: Using the Converse of the
Corresponding Angles Postulate
Use the Converse of the Corresponding Angles
Postulate and the given information to show
that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
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2-7 Flowchart and Paragraph Proofs
Holt Geometry
2-7 Flowchart and Paragraph Proofs
Example 2A: Determining Whether Lines are Parallel
Use the given information and the theorems you
have learned to show that r || s.
4  8
4  8
4 and 8 are alternate exterior angles
r || s
Conv. Of Alt. Ext. s Thm.
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2-7 Flowchart and Paragraph Proofs
Example 2B: Determining Whether Lines are Parallel
Use the given information and the theorems you
have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5
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2-7 Flowchart and Paragraph Proofs
Check It Out! Example 2b
Refer to the diagram. Use the given information
and the theorems you have learned to show
that r || s.
m3 = 2x, m7 = (x + 50),
x = 50
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2-7 Flowchart and Paragraph Proofs
Lesson Quiz: Part I
Name the postulate or theorem
that proves p || r.
1. 4  5
Conv. of Alt. Int. s Thm.
2. 2  7
Conv. of Alt. Ext. s Thm.
3. 3  7
Conv. of Corr. s Post.
4. 3 and 5 are supplementary.
Conv. of Same-Side Int. s Thm.
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