Be able to answer the questions on the following document:
- What is the difference between a line and a line segment? How do we represent these differences with symbols? A line goes on forever in both direction, a segment stops at its two endpoints. We use arrows on a line to show that it goes on forever.
- What is similar about how lines, segments, and rays are named? They all use the capital letters of two points on the figure, and a symbol above the two letters.
- What are the differences between the methods for naming lines, segments, and rays? Lines are named using any two points on the line. Segments need to be named using their endpoints. Rays have to start with their endpoint, and then use any second point anywhere along the ray. Each symbol is also different: Arrows for lines, one arrow for rays, and no arrows for segments.
- Why do we only use two points for naming rays, lines, and segments? Infinitely many lines go through any one given point, so one point is not enough. For two points, there is only one specific line connecting them, so it is enough information to describe an exact line. 3 or more points on the same line is more than you need, so we don’t use that.
- Why do we need 3 points to name a plane? Why can they not be collinear? For one or two points, there are infinitely many planes going through them. The same issue exists for three collinear points. Three points that are not collinear begin to describe a slice of space. Only one plane in space cuts through three not collinear points.
- Is there a distinction made between capital and lowercase letters in Geometry? Yes!
What about print and cursive? Why? Yes! We use different letters so that when you look at them on a diagram, we know that the lowercase cursive letter is describing a line, not a point, or that the uppercase cursive letter is for the plane, not some point on it. It’s to avoid confusion!
- Are opposite rays one or two things? Two things! Opposite rays are two rays. Opposite rays, although they create the shape of a line, they are not a line.
- What do we mean by the “intersection” of two things? The intersection of two things is the parts that they have in common.
- What does collinear mean? Coplanar? Collinear- on the same line; Coplanar- on the same plane.
- What objects/figures/ideas have quick symbols to represent them? What are the symbols?
- Which don’t have symbols?
- If a geometric figure can be named using either a symbol or a word, do we use both at the same time?
- What is a definition?
- What is an appropriate an answer to the request to “List 3 points”?
- Why are some parts of diagrams sometimes dotted lines instead of solid?
- If a geometric figure isn’t shown on a diagram, can you still reference it? How?