3.1.4 Properties of Perpendicular Lines (continued)

By the Lines Perpendicular to the Same Line Theorem, if two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

By the Linear Pair of Congruent Angles Postulate, if two lines intersect and form a linear pair such that the angles are congruent, then the lines are perpendicular.

Use the given information to prove that b ⊥ d . Notice that ∠ 1 and ∠ 2 form a linear pair. So, since ∠ 1 and ∠ 2 are congruent (Given) and form a linear pair (definition of linear pair), a ⊥ c by the Linear Pair of Congruent Angles Postulate. It is also given that a || b . So, since a ⊥ c and a || b , b must be perpendicular to c as well by the Perpendicular Transversal Theorem. Finally, since b ⊥ c and c || d (Given), b must be perpendicular to d as well by the Perpendicular Transversal Theorem.

150

Made with FlippingBook - Online magazine maker