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Big Ideas Math Integrated I, 2016 View details

4. Proofs with Perpendicular Lines

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Exercise 14 Page 525

Use the following figure.

See solution.

Practice makes perfect

In the following figure, it's given that m ⊥ p and n ⊥ p.

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	Reason
1. m ⊥ p, n ⊥ p	1. Given
2. m∠ 1 = 90^(∘), m∠ 2 = 90^(∘)	2. Definition of perpendicular lines
3. m∠ 1=m∠ 2	3. Transitive Property of Equality
4. ∠ 1 ≅ ∠ 2	4. Definition of congruent angles
5. m ∥ n	5. Corresponding Angles Converse