Download Geo 2.7 Flowchart and Paragraph Proof Student Notes

Geometry
Name:______________________
Date: ___________
Chapter 2: Geometric Reasoning
Section 2.7: Flowchart & Paragraph Proofs
Are you ready?
Complete each sentence.
1. If the measures of two angles are ________________, then the angles
are congruent.
2. If two angles form a ________________, then they are supplementary.
3. If two angles are complementary to the same angle, then the two angles
are ________________.
Objectives of Lesson: ________________________________________
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Who uses this? ___________________________________________
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A second style ___________________________________________
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Common Segments Theorem
Theorem
Hypothesis
Conclusion
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Example 1: Reading a Flowchart Proof
Use the given flowchart proof to write a two-column proof.
Given: 2 and 3 are comp.
1  3
Prove: 2 and 1 are comp.
Flowchart proof:
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Example 2: Reading a Flowchart Proof
Use the given flowchart proof to write a two-column proof.
Given: RS = UV, ST = TU
Prove: RT  TV
Flowchart proof:
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Example 3: Writing a Flowchart Proof
Use the given two-column proof to write a flowchart proof.
Given: B is the midpoint of AC.
Prove: 2AB = AC
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Example 4: Writing a Flowchart Proof
Use the given two-column proof to write a flowchart proof.
Given: 2  4
Prove: m1  m3
Two-column Proof:
A paragraph proof __________________________________________
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Theorems
Theorem
Hypothesis
Conclusion
Example 5: Reading a Paragraph Proof
Use the given paragraph proof to write a two-column 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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Example 6: Use the given paragraph proof to write a two-column proof.
Given: WXY is a right angle. 1  3
Prove: 1 and 2 are complementary.
Paragraph Proof: Since WXY is a right angle,
mWXY = 90° by the definition of a right angle. By
the Angle Addition Postulate, mWXY = m2 + m3.
By substitution, m2 + m3 = 90°. Since 1  3,
m1 = m3 by the definition of congruent angles.
Using substitution, m2 + m1 = 90°. Thus by the
definition of complementary angles, 1 and 2 are
complementary.
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Example 7: Writing a Paragraph Proof
Use the given two-column proof to write a paragraph proof.
Given: 1 and 2 are complementary
Prove: 3 and 4 are complementary
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Example 8: Writing a Paragraph Proof
Use the given two-column proof to write a paragraph proof.
Given: 1  4
Prove: 2  3
Two-column proof:
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