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

2. 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.

3. 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?

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

5. 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

6. 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

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

8. e f 1 2

9. 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.

10. 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).