Download Points, Lines, Planes and Angles - Homework Definition | MATH 120 and more Study notes Mathematics in PDF only on Docsity! Chapter 10. Section 1 Page 1 Section 10.1 – Points, Lines, Planes and Angles Homework (pg 513) 1-2, 5-36 • Definition: A point is represented as a small dot and usually written as a capitol letter (point A). It has no dimension, but merely specifies a place in space. • Definition: A line connects two distinct points with the shortest possible distance (in other words it is straight). It goes on forever in both directions. It is expressed with a lower case letter (line l) or using the letters of each point next to each other with a line above (line or AB BA suur suur ). • Definition: A plane is a flat surface with no boundaries, and it has no thickness. It is two- dimensional, meaning you can move two different directions on that surface. • Definition: We can take portions of lines. A line going in one direction is a ray. The ray has an initial point (where it begins) and a terminal point (to specify where it heads). It is expressed with the letters of the points (ray or AB BA uuur suuu , note the initial point has no arrow above it). A line segment is just the portion of the line between two points known as endpoints. It is expressed without arrowheads (line segment or AB BA ). • Note that lines and line segments can be written with either point first, but for a ray you have to be careful that the initial point has no arrowhead above it. • Definition: An angle is formed by two rays that meet at their initial points, which is known as the vertex of the angle. It has an initial side and a terminal side, which can be difficult to determine out of context. Most angles are written in standard position on the two-dimensional x-y axis, which is when the initial side is lined up with the positive x-axis and the vertex at the ordered pair (0,0) Angles are named several ways. You can name the angle with three points (the vertex B and one point on each ray, A&C) as or or ABC ABC ABC∠R S . Or you can just use the vertex as or or B B B∠R S . Sometimes there is a greek letter inside the angle (between initial and terminal sides) and you can use that letter or or β β β∠R S • You measure angles by finding the amount of rotation from the initial side to the terminal side. Angles can be measured in degrees (there are 360o in a circle) or radians (there are 2π radians in one circle, π is approximately 3.14). Fractional components of degrees are minutes (60 minutes = 1 degree) or seconds (60 seconds = 1 minute). This is the same as time measurements… why?
