4. Proofs with Perpendicular Lines
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Use the following figure.
See solution.
According to the Lines Perpendicular to a Transversal Theorem, in a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Thus, using the given information, we want to prove that m ∥ n. Let's write a two-column proof.
Statement
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Reason
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1. m ⊥ p, n ⊥ p
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1. Given
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2. m∠ 1 = 90^(∘), m∠ 2 = 90^(∘)
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2. Definition of perpendicular lines
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3. m∠ 1=m∠ 2
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3. Transitive Property of Equality
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4. ∠ 1 ≅ ∠ 2
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4. Definition of congruent angles
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5. m ∥ n
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5. Corresponding Angles Converse
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