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Big Ideas Math Integrated I, 2016 View details

5. Using Parallel and Perpendicular Lines

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Exercise 26 Page 532

Consider the Slopes of Perpendicular Lines Theorem.

Statements	Reasons
1. a and b are vertical lines.	1. Given.
2. a and b are perpendicular to a horizontal line c.	2. Slopes of Perpendicular Lines Theorem.
3. a and b are parallel lines.	3. Lines Perpendicular to a Transversal Theorem.

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Let a and b be two vertical lines, being cut by a horizontal transversal c. By the Slopes of Perpendicular Lines Theorem, a and b are both perpendicular to c.

Slopes of Perpendicular Lines Theorem a⊥ c and b⊥ c

By the Lines Perpendicular to a Transversal Theorem, we have that a and b are parallel lines.

Lines Perpendicular to a Transversal Theorem a∥ b We can summarize our proof in a two-column proof table.

Statements	Reasons
1. a and b are vertical lines.	1. Given.
2. a and b are perpendicular to a horizontal line c.	2. Slopes of Perpendicular Lines Theorem.
3. a and b are parallel lines.	3. Lines Perpendicular to a Transversal Theorem.

Subchapter links

Communicate Your Answer p.527

Monitoring Progress p.529-530

Exercises p.531-532

Exercise 26 Page 532

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