Lesson 2.1 Perpendicularity Objective: Recognize the need for clarity and concision in proofs and understand the concept of perpendicularity

From now on, when you write a two-column proof, try to state each reason in a single sentence or less. This chapter contains more definitions and theorems for you to memorize and use.

Perpendicular Lines, Rays and Segments Perpendicularity, right angles and measurements all go together. Definition: Lines, rays, or segments that intersect at right angles are perpendicular. What is the symbol for perpendicular?

Let’s Draw some examples of perpendicularity. b M H K J G F E D

Do NOT assume perpendicularity from a diagram! In DEF it appears that In the figure at the right, the mark inside the angle ( ) indicates that is a right angle. B A C It is also true that and Do NOT assume perpendicularity from a diagram! In DEF it appears that but we may not assume that they are. F E D

In each of the following, name the angles that can be proved to be right angles. X M K L J L W O S

Let’s practice Find the measure of M A C 2 1 Y X Z 3 4 S

e f 1 2

Do NOT assume perpendicularity from a diagram Important … Do NOT assume perpendicularity from a diagram Two perpendicular number lines form a two-dimensional coordinate system, or coordinate plane.

The horizontal line is called the x-axis y-axis A (3,4) The vertical line is called the y-axis Origin x-axis Each point is represented by an ordered pair in the form of (x,y) The values of the x and y are called the points coordinates The intersection of the axes is called the origin. Its coordinates are (0,0).