Beginning of Geometry Chapter 1

Service Description

I will have to cover the chapter for the impaired so it may cover more than one lesson. The rest can study the pictures given if they wish. There is another lesson with more pictures, then the exercises will be separate. This last picture you will just have to read Grandma's description of it because she can't get it good enough. Chapter 1 starts out by saying, "Studying geometry is very different from studying algebra. In geometry we are concerned with developing a logical structure in which mathematical relationships are 'proved' as well as 'applied.' In this chapter you will learn: " some basic terms and assumptions of geometry; nature of geometric proofs; the type of mathematical reasoning forming the course. Again, these are the sections of study, Building Blocks of Geometry, Definitions and Postulates, Inductive Verses Deductive Reasoning, IF ... Then ... Sentence Structure. (remember vocabulary terms will be marked with ' 'because Grandma cannot make it bold faced). Section Building Blocks of Geometry says, "Studying geometry is, in a sense, like building a house. Geometry uses logical reasoning as the cement and the following types of statements as the basic building blocks:" "Undefined Terms" in "that they cannot be defined using simpler terms. 'Point', 'line', and 'plane' are defined terms in geometry. Although these terms cannot be defined, they can be described. "Defined Terms." Are "new terms" that "can be defined using undefined as well as previously defined terms, thereby creating an expanding "dictionary" of terms which makes it easier to describe geometric figures and relationships." "Postulates." "Are so basic that they cannot be arrived at using simpler facts. A 'postulate' is a statement that is accepted without proof. (But I thought it was like a rule to follow.) They say, "For instance, the observation :Exactly one line can be drawn through two points" is a postulate." "Theorems," " Is a generalization that can be proved to be true. "Prove" simply means presenting a valid argument that uses a set of known facts and logical reasoning to show that a statement is true." As: "The sum of the measures of the three angles of a triangle is 180" is a theorem." "Geometry is an example of a 'postulational system' in which a beginning set of assumptions and undefined terms is used as a starting point in developing new relationships that are expressed as theorems. Grandma must go to another lesson to keep going because there is no room.