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Rule

Converse Perpendicular Transversal Theorem

If a transversal is perpendicular to two lines, the two lines are parallel.

Based on the diagram, the following statement holds true.

If t ⊥ l_1 and t ⊥ l_2, then l_1 ∥ l_2.

Proof

It is given that the transversal t is perpendicular to the lines l_1 and l_2. This means that the lines l_1 and t, and l_2 and t, intersect at a right angle.

Angles ∠ 1 and ∠ 2 are corresponding angles and they are congruent. By the Converse Corresponding Angles Theorem, l_1 and l_2 are parallel.

This proves the theorem.

If t ⊥ l_1 and t ⊥ l_2, then l_1 ∥ l_2.

Exercises

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