Section 1.1 – Identify Points, Lines, and Planes

Section 1.1 – Identify Points, Lines, and Planes

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Section 1.1 – Identify Points, Lines, and Planes

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1. Section 1.1 – Identify Points, Lines, and Planes Divide the top half of your paper into three vertical columns. The titles for the columns should be Points, Lines, and Planes Try to write a definition of each of these terms in your columns This is a difficult task as these are actually known as “undefined terms” in Geometry!

2. Section 1.1 – Identify Points, Lines, and Planes • What do we use to represent a point? • A point is represented by a dot • How many dimensions does a point exist in? • It has no dimensions (this will make more sense soon) • What is the best way to communicate to someone which point we are talking about in the diagram? • We label each point with a Capital letter

3. Section 1.1 – Identify Points, Lines, and Planes • What do we use to represent a point? • A point is represented by a dot • How many dimensions does a point exist in? • It has no dimensions (this will make more sense soon) • What is the best way to communicate to someone which point we are talking about in the diagram? • We label each point with a Capital letter • Example: Point B

4. Section 1.1 – Identify Points, Lines, and Planes • How do we represent a line? • An infinite number of dots (points) put together in a straight row with arrows on the ends • Why the arrows? • A line extends forever in both directions • How many dimensions does a line exist in? • One dimension (left-right is one dimension, up-down is another, and forward-backward is another)

5. Section 1.1 – Identify Points, Lines, and Planes • How do we name a line? • Option one: a single lowercase letter • Example: line m • Option two: name two points on the line • Example: line FC • Or put a little line WITH TWO ARROWS on top of the points like

6. Section 1.1 – Identify Points, Lines, and Planes • How do we represent a plane? • Something that looks like a floor or wall (but really extends forever) • How many dimensions? • A plane exists in two dimensions • What is it called if it goes forever in three dimensions? • Space • Sometimes to emphasize the three dimensions we call it “3-space”

7. Section 1.1 – Identify Points, Lines, and Planes • How do we name a plane? • Option one: a single letter (that is not referencing a point) • Example: plane R • Option two: three points that are NOT in a straight line, but are on the plane • Example: plane EFG

8. Section 1.1 – Identify Points, Lines, and Planes • More definitions: • Collinear • Points that are all on a line together • Noncollinear = NOT on the same line • Coplanar • Points, lines, etc. that are all on a plane together • Noncoplane = NOT on the same plane

9. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Give two other names for • Give two other names for plane O • Name three collinear points • Name four coplanar points

10. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Give two other names for = line t, • Give two other names for plane O = plane WEM, plane WKM • Name three collinear points = W, E, K • Name four coplanar points = W, E, K, M

11. Section 1.1 – Identify Points, Lines, and Planes • (Add under Line) • Line = contains points extending forever in two directions, notation has two arrows • Ex: same as • Line segment = contains points between two endpoints, notation has no arrows • Ex: same as • Ray = contains points from one point extending forever in one direction, notation has one arrow on the right (and order of letters must be endpoint, then other point) • Ex: NOT the same as

12. Section 1.1 – Identify Points, Lines, and Planes • What do you think it would take for two rays to be opposite rays? • They have to have the same endpoint and go in completely opposite directions • Thus opposite rays are collinear

13. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Name two opposite rays • or • Give another name for • True or false: is the same as • False • True or false: is the same as • True

14. Section 1.1 – Identify Points, Lines, and Planes • What is formed when two different lines intersect? • A point, like point P

15. Section 1.1 – Identify Points, Lines, and Planes • What is formed when two different planes intersect? • A line, like • Things to notice in the drawing: • You can only “see” the shading of the plane “on top” • The dashed lines represent the part of the plane that you cannot see

16. Section 1.1 – Identify Points, Lines, and Planes • Examples: • Sketch a plane and a line that is in the plane • Sketch a plane and a line that does not intersect the plane • Sketch a plane and line that intersects the plane at one point

17. Closure On a half sheet of paper (to turn in when you are finished) write down: 3 vocabulary words from today’s lesson A drawing of 2 planes intersecting 1 question that you have Homework: page 5 #3-13, 17-23, 44