2.2 Review Worksheet (continued)
21. Use the given paragraph proof to write a two-column proof. Given : ∠ 1 ≅ ∠ 4 Prove : ∠ 2 and ∠ 3 are supplementary. Paragraph proof: ∠ 4 and ∠ 3 form a linear pair, so they are supplementary by the Linear Pair Theorem. Therefore, m ∠ 4 + m ∠ 3 = 180º. Also, ∠ 1 and ∠ 2 are vertical angles, so ∠ 1 ≅ ∠ 2 by the Vertical Angles
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2 5
4 6 3
Theorem. It is given that ∠ 1 ≅ ∠ 4. So by the Transitive Property of Congruence, ∠ 4 ≅ ∠ 2, and by the definition of congruent angles, m ∠ 4 = m ∠ 2. By substitution, m ∠ 2 + m ∠ 3 = 180º, so ∠ 2 and ∠ 3 are supplementary by the definition of supplementary angles.
22. Use the given two-column proof to write a paragraph proof. Given : ∠ 1 and ∠ 2 are complementary. Prove : ∠ 2 and ∠ 3 are complementary. Two-column proof:
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1
3
Statements
Reasons
1. ∠ 1 and ∠ 2 are complementary. 2. m ∠ 1 + m ∠ 2 = 90º 3. ∠ 1 ≅ ∠ 3 4. m ∠ 1 = m ∠ 3 5. m ∠ 3 + m ∠ 2 = 90º 6. ∠ 2 and ∠ 3 are complementary.
1. Given 2. Def. of comp. ∠ s 3. Vert. ∠ s Thm. 4. Def. of ≅ ∠ s 5. Subst. Steps 2, 4 6. Def. of comp. ∠ s
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