Transcript Applied Geometry

Geometry
Lesson 1 – 1
Points, Lines, and Planes
Objective:
Identify and model points, lines, and planes.
Identify intersecting lines and planes.
Undefined terms
Undefined terms: objects that are only
explained using examples and
descriptions.
Point
 Line
 Plane

Point
Point:
A
point is a location.
 Has neither shape nor size
Named:
 Capital
letter
Example
 Point
A
Line
Line:
Made up of points
 Has no thickness or width
 Exactly one line through and two points.

Named:
Any 2 points on the line (2 capital letters)
 Lowercase script letter

Example

line m

PQ
or
QP
Plane
Plane:
A flat surface made up of points that extends
infinitely in all directions.
 Exactly one plane through any 3 points not on the
same line.

Named
Capital Script letter
 3 points on the plane not on a line (3 capital letters)

Example
K


Plane BCD (any order)
Definitions
Collinear:

Points that lie on the same line
Noncollinear:

Points that do not lie on the same line.
Coplanar

Points that lie in the same plane
Noncoplanar

Points that do not line in the same plane
Use the figure to name
each of the following:
A line containing point W
Any one of the following work:
line n, VW ,WV ,VX , XV ,VY ,
YV ,WX , XW ,WY , YW , XY , YX
A plane containing point X
Any one of the following work: (3 letters that are noncollinear)
P, plane XZY, plane VZY, plane VZW,
plane WZX, plane VZX, Plane WZY
Example
Name the geometric term modeled by the
objects in the picture.

Push pin
Point G

Maroon boarder

The card itself
HJ
Sample: plane FGJ

Stripes on a sweater

Corner of a box
point
lines
Intersection
Intersection of two or more geometric figures is
the set of points they have in common.
Where do two lines intersect? At a point.
Where do two planes intersect?
At a line
Draw the following
QR intersects plane T at point S.
Sample answer
Must have the dashed line to show that the line goes through
the plane and is not on or in the plane.
Draw the following
Line p lies in plane N and contains point L.
Sample answer.
Definitions
Definitions are defined terms that are
explained using undefined terms and/or
other defined terms.
Space: defined as a boundless, threedimensional set of all points. Space can
contain lines and planes.
How many planes appear
in this figure.
6 planes: 5 around the pyramid and one on
bottom of the the pyramid… don’t name the
bottom plane twice.
Name 3 points that are collinear.
Points J, K, and D
Make sure you have commas otherwise it names a plane.
Name the intersection of plane HDG with plane
X.
HG
At what point do LM and EF intersect? Explain.
Don’t appear to intersect since L is the only point on
line LM in the plane.
Are points E, D, F,
and G coplanar?
No, not all on the same plane.
At what point or in what line do
planes JDH, JDE, and EDF intersect?
Point D is the only thing in common.
Homework
Pg. 8 1 – 12 all, 14 – 46 EOE,
52, 66 – 82 EOE