Bellwork Juan has more than 5 but fewer

Bellwork • Juan has more than 5 but fewer than 11 fish in his aquarium. Write an inequality to express the number of fish in his aquarium • Draw a line using only dots • Kansas City rests at 231 m above sea level. Find this elevation in feet.

Bellwork Solution Juan has more than 5 but fewer than 11 fish in his aquarium. Write an inequality to express the number of fish in his aquarium

Bellwork Solution • Draw a line using only dots

Bellwork Solution • Kansas City rests at 231 m above sea level. Find this elevation in feet.

Identify Points, Lines and Planes Section 1. 1

The Concept • Before we begin discussing advanced geometric principles, we must start with the basics • Basics provide the foundation for understanding • We then define the four undefined terms

Question What is your name? • How did we figure this out? Roster Enrollment Form 111 -22 -3333 • Before the Social Security System, names where associated with the father, but also with regions, vocations or former masters and owners

Definitions • Definition – Way of describing a thing or concept – Based upon an agreed upon consensus of terminology • Connotation • Denotation Definition 1 -1 Way of describing a thing or concept Based upon an agreed upon consensus of terminology

Geometric Definitions • The basis of geometry rests in four basic terms – Called the undefined terms, because they lack previous basis

Undefined Terms • Space – Collection of all points – All objects exist in space • Point – • Line – – Connections of dots in a direction Unbounded i. e. continues on forever Two points define a line A The two points name the line B

Undefined Terms • Plane – – – A Two dimensional object Unbounded m C Flat “sheet” Three non-collinear points define a plane These three points also name the plane Can also be named by a single letter B

Definitions Colinear 1 -1 Points that are on the same line Coplanar 1 -1 Points that are on the same plane

Using the undefined terms • Example 1

Defined Terms • The undefined terms give us other basic definitions • Segment – Portion of a line that exists between two endpoints – Named by those two points – Written with a line over the top • Ray B A – Portion of a line that starts at an endpoint and extends on indefinitely – Unbounded on one side – Named by two points A – Written as B

Important Distinction • Direction is important to Rays but not to Segments – Why? B A

Definitions • Opposite Rays – Rays that go in opposite directions – What is the opposite ray of CB B C A

Definitions • What is the common thing between these two circles? • Geometry is no different – What is the shared point of these two lines? C A B

Definitions • Intersections – Points that are shared amongst two geometric figures A B – Line AB is the set of shared points of these two planes

Homework • 1. 1 – 1, 2, 3 -13, 14 -32 even, 40 -42, 44

Homework G F D C A B

Most Important Points • Undefined Terms – – Space Point Line Plane • Defined Terms – Segment – Ray • Definition of colinear and coplanar • Concept of intersectionality • Naming Scheme for subsequent figures