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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 2 Page 522

∠ 2 and ∠ 7 are alternate exterior angles.

See solution.

Practice makes perfect

According to the Perpendicular Transversal Theorem, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

In the diagram ∠ 2 and ∠ 7 are alternate exterior angles, and according to the Alternate Exterior Angles Theorem such angles are congruent since h∥ k.

As we can see, k and h are both perpendicular to j.

Statement	Reason
1. h∥ j, j⊥ h	1. Given
2. m∠ 2=90^(∘)	2. Definition of perpendicular lines
3. ∠ 2≅ ∠ 7	3. Alternate Exterior Angles Theorem
4. m∠ 2= m∠ 7	4. Definition of congruent angles
5. m∠ 7=90^(∘)	5. Transitive Property of Equality
6. j⊥ k	6. Definition of perpendicular lines

Subchapter links

Communicate Your Answer p.519

Monitoring Progress p.520-523

Exercises p.524-526