Chapter 1: Introduction to Plane Geometry

Section 1.1:Geometric Figures Geometry-the study that deals with the properties, measurements, and construction of flat figures, such as angles, triangles, and of solid figures, such as cubes, pyramids, and spheres.

Rectangular Block Each of the six faces is called a surface The intersection of two surfaces is called an edge In a geometric solid, these edges are called lines Therefore, a line is the intersection of two surfaces

Rectangular Block In a geometric solid, the vertices are called points A point is the intersection of any two lines Solids, surfaces, and lines are geometric figures Their form or shape is considered as well as their size The magnitude of a figure refers to its size or extent

The straight line is one of the most fundamental concepts in geometry The instrument used to draw straight lines is called a straight edge A surface is a plane if the straight line joining any two of its points lies wholly within the surface

Section 1.2:The Line Unless otherwise stated, the word line will mean straight line. Principle 1: A straight line is the shortest line between two points Principle 2:Only one straight line can be drawn between two points Two points determine a straight line If we attempted to draw two straight lines between two points, they would be the same line—they would coincide Principle 3: Two straight lines can intersect at only one point

Section 1.3: The Line Segment A limited portion of a line is called a line segment or simply a segment A line which is limited in only one direction is called a ray Two line segments are equal when their end points can be made to coincide A line segment is bisected by a point when it is divided into two equal parts by the point. The point is called the midpoint. A line segment is trisected when two points divide it into three equal parts Lines are best measured by means of a compass

Example/Exercises Divide a 4-inch line into two parts so that one part is 1.5 inches longer than the other. 1. Divide a 5-inch line into two parts so that one part is (a) 2.25 inches shorter than the other, (b) 3 times the other. 2.Divide a 5.25 inch line into three parts whose ratios are 1:2:3.

Exercises 5. If we represent the length of a line by a, how may we represent the length of a line that is 3 inches longer? If the combined length of the two lines is 15 inches, what is the length of each line? 7. If .25 in. represents 1 ft., what distances are represented by lines of the following lengths: 2 in. 5 in. 1.5 in. 2.75 in. 4.875 in.

Exercises 8. The distance between New York and San Francisco is about 3200 miles. How far apart would these two places be on a map drawn to a scale of 1 in. to 200 mi.?

Constructions Lines or figures formed using only a compass and a straight edge Constructions begin with some information, such as a line or angle, and then require you to use those elements to construct a figure. Lines can be added and subtracted by construction.

Example Construct a line equal to the sum of the two given lines a and b.

Homework 1.3 B # 3,4,6,9,11 1.3 C # 2-4 Due tomorrow at the beginning of class.