Big Ideas Math Integrated I, 2016
BI
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