Download Geometry Lecture Notes: Points, Lines, Planes and Angles - Prof. Sandra Nite and more Study notes Mathematics in PDF only on Docsity! Section 9-1 1 Math 366 Lecture Notes Section 9.1 – Basic Notions (of Geometry) The fundamental building blocks of geometry are points, lines, and planes. These terms are not formally defined, but are described intuitively. (see p. 573). Linear Notions In geometry, a line has no thickness, and it extends forever in two directions. It is determined by two points. Collinear points are points on the same line. (Any two points are collinear but not every three points have to be collinear.) A point C is between points A and B if C ≠ A, C ≠ B, and C is on the part of the line flanked by A and B. Alternate Definition: Point B is between points A and C if A, B, and C are collinear and the sum of the distances from A to B and B to C equals the distance from A to C. A line segment is a subset of a line that contains two points of the line and all points between those two points. Notation: AB or BA . A ray is a subset of a line that contains the endpoint and all points on the line on one side of the point. Notation: AB Planar Notions A plane has no thickness, and it extends indefinitely in two directions. A plane is determined by three points that are not all on the same line. In other words, given three noncollinear points, a unique plane is determined. Points in the same plane are coplanar. Noncoplanar points cannot be placed in a single plane. Lines in the same plane are coplanar lines. Skew lines are lines that do not intersect, and there is no plane that contains them. Intersecting lines are two coplanar lines with exactly one point in common. Concurrent lines are lines that contain the same point. Two distinct coplanar line m and n that have no points in common are parallel lines. Notation: m // n. Section 9-1 2 How many different lines can be drawn through two points? Can skew lines be parallel? Why or why not? On a globe, a “line” is a great circle, that is, a circle the same size as the equator. How many different lines can be drawn through two different points on a globe? Properties of Points, Lines, and Planes • There is exactly one line that contains any two distinct points. • If two points lie in a plane, then the line containing the points lies in the plane. • If two distinct planes intersect, then their intersection is a line. • There is exactly one plane that contains any three distinct noncollinear points. • A line and a point not on the line determine a plane. • Two parallel lines determine a plane. • Two intersecting lines determine a plane. Find the number of lines determined by 8 points, no 3 of which are collinear. Polya’s Four Step Problem-Solving Process (pp. 4, 18) 1. Understand the problem. 2. Devise a plan. 3. Carry out the plan. 4. Look back. tennis ball paper folding paper folding intertwine fingers three heads point, pencil, paper two pencils two pencils tennis ball tennis ball
