1. 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
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2. 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
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3. 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 The perpendicular bisector of a line segment is unique.
Exercise 2 p. 50
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