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Big Ideas Math Integrated I, 2016 View details

4. Proofs with Perpendicular Lines

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Exercise 13 Page 525

Use the following figure.

See solution.

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In the following figure it's given that ∠ 1 ≅ ∠ 2.

According to the Linear Pair Perpendicular Theorem, if two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Thus, using the given information, we want to prove that g ⊥ h. Let's write a two-column proof.

Statement	Reason
1. ∠ 1 ≅ ∠ 2	1. Given
2. m∠ 1 = m∠ 2	2. Definition of congruent angles
3. m∠ 1+m∠ 2=180^(∘)	3. Linear Pair Postulate, according to the diagram
4. m∠ 1+m∠ 1=180^(∘)	4. Substitution Property of Equality
5. 2m∠ 1=180^(∘)	5. Distributive Property
6. m∠ 1=90^(∘)	6. Distributive Property of Equality
7. g ⊥ h	7. Definition of perpendicular lines

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Communicate Your Answer p.519

Monitoring Progress p.520-523

Exercises p.524-526

Exercise 13 Page 525

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