Exercise 13 Page 525

In the following figure it's given that $∠ 1 ≅ ∠ 2 .$

According to the Linear Pair Perpendicular Theorem, if two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. Thus, using the given information, we want to prove that $g ⊥ h .$ Let's write a two-column proof.

Statement	Reason
$∠ 1 ≅ ∠ 2$	Given
$m ∠ 1 = m ∠ 2$	Definition of congruent angles
$m ∠ 1 + m ∠ 2 = 18 0^{\circ}$	Linear Pair Postulate, according to the diagram
$m ∠ 1 + m ∠ 1 = 18 0^{\circ}$	Substitution Property of Equality
$2 m ∠ 1 = 18 0^{\circ}$	Distributive Property
$m ∠ 1 = 9 0^{\circ}$	Distributive Property of Equality
$g ⊥ h$	Definition of perpendicular lines