Exercise 2 Page 522

According to the Perpendicular Transversal Theorem, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

In the diagram $∠ 2$ and $∠ 7$ are alternate exterior angles, and according to the Alternate Exterior Angles Theorem such angles are congruent since $h ∥ k .$

As we can see, $k$ and $h$ are both perpendicular to $j .$

Statement	Reason
$h ∥ j, j ⊥ h$	Given
$m ∠ 2 = 9 0^{\circ}$	Definition of perpendicular lines
$∠ 2 ≅ ∠ 7$	Alternate Exterior Angles Theorem
$m ∠ 2 = m ∠ 7$	Definition of congruent angles
$m ∠ 7 = 9 0^{\circ}$	Transitive Property of Equality
$j ⊥ k$	Definition of perpendicular lines