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Rule

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line as well.

Based on the diagram, the following statement holds true.

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

Proof

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

Angles ∠ 1 and ∠ 2 are corresponding angles. By the Corresponding Angles Theorem, ∠ 1 and ∠ 2 are congruent. This means that ∠ 2 is also a right angle.

Therefore, t is perpendicular to l_2. This proves the theorem.

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

Exercises

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