Rest of Geometry's Chapter1 pt 1

Service Description

Read more of the Chapter 1 pages of Geometry and study Chapter 1 and record anything necessary. Notice Chapter is a "CH" word. The Exercise questions will be on Friday. At this point the book was talking about 'definitions of Collinear and noncollinear points. The book goes on saying, "Notice that a definition begins by identifying the term being defined. The definition of 'collinear points' uses only geometric terms (points and line) that have been previously discussed. Contrast this definition with the following one: An 'apothem' is a line segment drawn from the center of a regular polygon perpendicular to a side of the polygon." This is not a good definition. For it is not only clear what an apothem but does not explain a 'regular polygon is or perpendicular and non of them have been explained. "Much of geometry involves building on previously discussed ideas." We can arrive at a definition of a triangle by starting with three noncollinear points (Figure 1.7a) and connect them with line segments, Directions we all can understand and since most of us have handled something in our lives, known as a 'Triangle' that when we hear these form a 'triangle' of Figure 1.7b we know what they are talking about mentioning it has the sides _____,____, and____. AB BC AC Therefore, when they say 'triangle' ABC we know what they are talking about. In continuation with the Definition of 'Triangle.' The professor says, "A 'triangle' is a figure formed by connecting three noncollinear points with three different line segments each of which has two of these points as end points. Notice that the definition uses the term 'noncollinear', which has been defined. Is it necessary to include that the three noncollinear points are connected by line segments." Yes, because in the case of this lumped up, swirled, and curved triangle of Figure 1.8 that most can see it is possible to join three non collinear points without using line segments. For the one side AB is a curve BC is lumpy, and AC has a loop in it. Yet this figure can still be connected by dots and have the shape of a funny looking 'triangle'. (Now we are going to the next lesson.)