1-2 Points, Lines, & Planes

9/16 1-2 Points, Lines, & Planes Objective: To understand basic terms of Geometry

Warm up: You are about to see a video. Watch it closely and count the number of passes the white shirt teams make. Watch This Video Closely

So you know what to look for now right? Okay… Try again.

Note To Students…(this does not need to be copied into your notes) Attention to detail will make the difference between a passing and a failing grade in this chapter. Every minute detail will count. So pay close attention to the details!!! They will be in pink throughout the notes.

A Point *Is like a location *Is represented by a dot *Is named with a capitalletter *Has no size When naming more than one you must use commas

*Is a series of points that extend in opposite directions without end. *Is named by any two points on the line or by single lowercase letter. Symbol is used over the Top of the two letters. A line

*Is a flat surface that has no thickness. *Contains many lines & extends without end in all directions. *Named by either a single capital letter (not a point) or by at least three points that are not on the same line. Plane

Collinear Point on the same line If your asked if points are collinear and out of 100 points 99 of them are on a line and one of them is not, then it’s a non-collinear situation. Coplanar Point on the same plane

Problem 1 (A) What are two other ways to name (b) What are two other ways to name plane P? (c) What are the names of three collinear points? What are the names of four coplanar points?

A Segment • Part of a line • Consists of the endpoints and all points between them. • Symbol is used over the two endpoint of the segment to name it.

Part of a line • Consists of one endpoint and all points extending in one direction. • Naming it: Endpoint as the first letter any other point on the ray as the second. • Symbol is used over the top A Ray

Opposite Rays • Two rays with the same endpointsthat extends in opposite directions • (always forms a line) • Named by their shared endpoint & any other point on each ray. Q Are Explain. S R

Problem 2 What are the names of the segments? What are the names of the rays? Which of the rays in part (b) are opposite rays?

Additional Examples What are 2 other ways to name What are 2 ways to name plane Q? What are the names of 3 collinear pts? What are the names of 4 coplanar pts?

Additional Examples Continued 2. What are the names of the segments? What are the names of the rays? Which of the rays are opposite rays?

Homework 1-2 P. 16 #s 1-14, omit #3

1-2 Points, Line & Planes Objective: To understand basic postulates (facts) of Geometry

Postulate or Axiom Is an accepted statement of fact We must never forget the facts of geometry because sometimes a diagram or a demonstration of a geometry topic may “look” to show one thing when in reality something completely different is happening.

Through any 2 points there is • exactly 1 line • If two distinct lines intersect, • then they intersect in exactly • 1 point. • If two distinct planes intersect, • then intersect in exactly one line Postulates

Problem 3 Each surface of the box represents part of a plane. What is the intersection of plane ADC and plane BFG? (b) What are the names of two planes that intersect in

Postulates-Continued • Through any three non-collinear points there is exactly one plane

Problem 4 (a.) What plane contains Points N, P, and Q? Shade the plane. (b,) What plane contains points J, M, and Q? Shad the plane.

Problem 4 (c.) What plane contains Points L, M, and N? Shade the plane. (b,) What is the name of a line that is coplanar with and ?

Additional Examples Continued Which plane contains points, J, M, and L? Which plane contains points L, P, and Q?

Additional Examples Continued What is the intersection of plane AEH and plane EGH?

Homework Page 16 3, 15-22, 27-32, 40-45

1-2 Points, Lines, & Planes