1 6 Relationships Perpendicular Lines Vertical lines extends

1. 6 Relationships: Perpendicular Lines • Vertical lines: extends up and down • Horizontal line: extends left to right • Perpendicular lines are two lines that meet to form congruent adjacent angles • Theorem 1. 6. 1: If two lines are perpendicular, then they meet to form right angles. –Proof is Example 1, p. 47 10/31/2021 1

Relationships: Properties • Relation “connects” two elements of an associated set of objects. – Table 1. 8 p. 47 • Reflexive: (one object) a R a – Equality is reflexive (Ex. 5 = 5) • Symmetric: (two objects) if a R b then b R a – Equality: (Ex. If 2 x = 5 then 5 = 2 x) – Perpendicularity of lines: ( l m , then m l) • Transitive: (three objects) if a R b and b R c then a R c. – Equality and Inequality: if x < y and y < z then x< z – Congruence of Angles: 1 2 and 2 3 then 1 3 10/31/2021 2

Theorems involving Perpendicular Lines • Theorem 1. 6. 2: If two lines intersect, then the vertical angles formed are congruent. – Ex. 3 p. 49 – Construction: Construct the line perpendicular to a given line at a specified point on the given line. p. 49 • Theorem 1. 6. 3: In a plane, there is exactly one line perpendicular to a given line at any point on the line. • Theorem 1. 6. 4 The perpendicular bisector of a line segment is unique. Exercise 2 p. 50 10/31/2021 3