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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.
Two parallel lines and a transversal perpendicular to them

Based on the diagram, the following statement holds true.

If and then

Proof

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

Two parallel lines and a transversal perpendicular to one of them

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

Two parallel lines and a transversal perpendicular to both of them

Therefore, is perpendicular to This proves the theorem.

If and then