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 1/17/2019

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 2x = 5 then 5 = 2x) 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 1/17/2019

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 1/17/2019