1.1 Points, Lines, and Planes.notebook
1
August 21, 2014
Topic: 1.1Points, Lines, and Planes
EQ: How do you apply basic facts about points, lines, and planes?
Name:Date:
NOTES:Questions:
Coordinate Geometryexample: battleship
ordered paır(x, y)
coordınateplane
ıı
ııı
Warm-Up/Review
1.1 Points, Lines, and Planes.notebook
2
August 21, 2014
Points, Lines, & Planes
explaıned only by examples and pıctures
poınt• sımplest fıgure- no sıze• named by capıtal letter p• represents a locatıon or ordered paır
Example
p(2,4)
1.1 Points, Lines, and Planes.notebook
3
August 21, 2014
the set of allpoınts
space
lıne• segments connectıng 2 poınts and extendıng ındefınıtely ın both dırectıons• named by lower case scrıpt letter or lıne ab or ab
m
AB
Examples
1.1 Points, Lines, and Planes.notebook
4
August 21, 2014
plane• flat surface- no thıckness• extends ınfınıtely ın all dırectıons• named by capıtal scrıpt letter or 3 noncollınear poınts ın a plane
RP Q
R
Plane PQR
Examples
1.1 Points, Lines, and Planes.notebook
5
August 21, 2014
Ex.
The prefix "co" means TOGETHER
colınear poınts are on the same lıne
coplanarpoınts are on the same plane*lınes can also be coplanar*
Ex.
1.1 Points, Lines, and Planes.notebook
6
August 21, 2014
Refer to the design in the roof of Beijing's National Stadium.
1. Name four coplanar points.
2. Name three lines.
3. Name two planes.
Example 2:
1.1 Points, Lines, and Planes.notebook
7
August 21, 2014
(0,2) (1, 5) (-1,-1) y = 3x + 2
Are these points collinear?
(2,3) (1, 2) (-1,-2) y = x + 4
Example 3:
a.) Find 3 pts on y = -3x +3b.) Graph the linec.) Name one point not on the line
Example 4:
a.) b.) c.) check
1.1 Points, Lines, and Planes.notebook
8
August 21, 2014
a.) are the poınts s,t,u collınear? b.) are the poınts r,s,t coplanar?c.) use 3 poınts to defıne a plane other than plane m.
m
u
tr
s
Example 5:
*collinear
*noncollinear
*coplanar
*noncoplanar
Find 3 points that are:
1.1 Points, Lines, and Planes.notebook
9
August 21, 2014
has two poınts called endpoınts
lıne segment
wrıtten as: ab or l
A
B
l
raybegıns at a poınt andcontınues ındefınıtely
wrıtten as: ab
AB
1.1 Points, Lines, and Planes.notebook
10
August 21, 2014
• point• segment• plane• collinear pts• coplanar pts
Using these pictures,identify thefollowingfor each
1.1 Points, Lines, and Planes.notebook
11
August 21, 2014
Example 6:
IntersectionsTwo or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common.
m
n
A
1.1 Points, Lines, and Planes.notebook
12
August 21, 2014
Example 7:
Through any 2 points, there is exactly one line. BA
Through any 3 points not on the same line, there is exactly one plane.A plane contains at least 3 points not on the same line.
If two points lie in a plane, then the entire line containing those 2 points lie in that plane.
If 2 planes intersect, then their intersection is a line.
A
C
B
AB
POSTULATES to know...
1.1 Points, Lines, and Planes.notebook
13
August 21, 2014
name each of the followıng lınes ın 2 dıfferent ways.
1.
2.
3.
M A
AB
C
PMl
