Applied Geometry
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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