1. Chapter 6: Inequalities in Geometry
6.2 – Inverses and Contrapositives
6.3 – Indirect Proofs (proof by contradiction)
6.4 – Triangle Inequalities

2. 6.3 – Indirect Proofs (Proofs by Contradiction)
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Contradictions:
6.3 – Indirect Proofs (Proofs by Contradiction)
1) “You are an unique individual – just like everybody else.”
2) An accurate estimate.
3) Hiding in plain sight.
4) The right to bear arms leads to less gun violence.

3. 6.3 – Indirect Proofs (Proofs by Contradiction)
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Template:
6.3 – Indirect Proofs (Proofs by Contradiction)
1) Assume temporarily that the conclusion (trying to prove) is FALSE.
2) Then reason logically until you reach a contradiction of a known fact (the given).
3) Therefore, the assumption is false, so the conclusion (trying to prove) is TRUE.

4. 6.3 – Indirect Proofs Example 1: Given: Mr. Cheng is in college.
Prove: Mr. Cheng graduated high school or equivalent.
Assume temporarily: Mr. Cheng did not graduate from high school.
Then: Mr. Cheng would not be in college if he did not graduate from high school or equivalent.
This contradicts the given that Mr. Cheng is in college.
Therefore: The assumption is false, so Mr. Cheng did graduate from high school or equivalent.

5. 6.3 – Indirect Proofs Example 2: Given: 2r + 3 ≠ 17 Prove: r ≠ 7
Assume temporarily: r = 7
Then: 2r + 3 = 2(7) + 3 = = 17.
This contradicts the given that 2r + 3 ≠ 17.
Therefore: The assumption is false,
so r ≠ 7.

6. Example 3: Given: quad ABCD with AB ≇ BC
6.3 – Indirect Proofs
Example 3: Given: quad ABCD with
AB ≇ BC
Prove: quad ABCD is not a rhombus.
Assume temporarily: quad ABCD is a
rhombus.
Then: all sides are ≅, so AB ≅ BC.
This contradicts the given that AB ≇ BC.
Therefore: The assumption is false,
so quad ABCD is not a rhombus.

7. Textbook Practice
Page 210: Classroom Exercises: #1-9