Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines , then it is perpendicular to the other line also.

Math diagram

Given:

$k ∥ l, t ⊥ k$

Prove:

$t ⊥ l$

Proof

	Statement	Reason
1	$k ∥ l, t ⊥ k$	Given
2	Let the angle between the lines $t$ and $k$ be $1$ and that between $t$ and $l$ be $2$ . $∠ 1$ is a right angle	Definition of perpendicular lines
3	$m ∠ 1 = 90 °$	Definition of right angle
4	$∠ 1 ≅ ∠ 2$	Corresponding angles
5	$m ∠ 1 = m ∠ 2$	Definition of congruent angles
6	$m ∠ 2 = 90 °$	Substitution Property
7	$∠ 2$ is a right angle	Definition of right angle
8	$t ⊥ l$	Definition of perpendicular lines

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