Use the Slopes of Perpendicular Lines Theorem to form expressions of the slopes.
See solution.
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If lines a and b are both perpendicular to line c, we can, by the Slopes of Perpendicular Lines Theorem, say that
m_a* m_c=- 1 and m_b* m_c=- 1.
By the Transitive Property of Equality we can equate these products:
m_a* m_c=m_b* m_c.
Using the Division Property of Equality we conclude that m_a=m_b. Finally, by the Slopes of Parallel Lines Theorem we have that a ∥ b.
