# 1.2 Points_ Lines and Planes by yaofenjin

VIEWS: 11 PAGES: 25

• pg 1
```									1.1 Points, Lines and
Planes
Honors Modern Geometry
Mr. Sgroi
Using Undefined terms and
definition
A definition uses known words to describe a
new word. In geometry, some words
such as point, line and plane are
undefined terms or not formally defined.
Using Undefined terms and
definition

• A point has no
dimension. It is        A

usually represented
Point A
by a small dot.
Using Undefined terms and
definition
• A line extends in one
dimension. It is                         l
usually represented
by a straight line with                 A

indicate that the line
extends without end
B
in two directions. In         Line   l or AB
this book, lines are
always straight lines.
Using Undefined terms and
definition
A plane extends in two
dimensions. It is usually
represented by a shape
that looks like a tabletop          A
or wall. You must
imagine that the plane
C
extends without end even       B
though the drawing of a
plane appears to have
edges.
Plane M or plane ABC
A few basic concepts . . .
 Must be commonly understood without
being defined. One such concept is the
idea that a point lies on a line or a plane.
 Collinear points are points that lie on the
same line.
 Coplanar points are points that lie on the
same plane.
Ex. 1: Naming Collinear and
Coplanar Points
a.   Name three points
H
that are collinear
G

Solution:                 D       E

D, E and F lie on the
same line, so they
are collinear.
Ex. 1: Naming Collinear and
Coplanar Points
b.   Name four points that
are coplanar.                     H

G

Solution:
D       E
D, E, F, and G lie on the
same plane, so they are
coplanar. Also D, E, F,
and H are coplanar;
although, the plane
containing them is not
drawn.
Ex. 1: Naming Collinear and
Coplanar Points
c.   Name three points
that are not                 H

collinear.               G

E
Solution:                 D

There are many correct
instance, points H,
E, and G do not lie
on the same line.
More . . .
   Another undefined
concept in geometry is                  l
the idea that a point on a
line is between two other
points on the line. You
can use this idea to
define other important
terms in geometry.
   Consider the line AB
Line   l or AB
(symbolized by AB).
More . . .                 A                        B

   The line segment or        Segment AB

segment AB                                          l
(symbolized by AB)                        B
consists of the
endpoints A and B,
and all points on AB
that are between A          A
and B.                                  Line   l or AB
More . . .                    A            B

   The ray AB                    Ray AB

(symbolized by AB)                                    l
consists of the initial                      B
point A and all points
on AB that lie on the
same side of A as
point B.                       A
Line   l or AB
More . . .                      A                    B

   Note that AB is the    Ray BA
same as BA and AB is                       l
the same as BA.                   B
However, AB and BA
are not the same.
They have different
initial points and      A
extend in different             Line   l or AB
directions.
More . . .
 If C is between A and B,
then CA and CB are
l
opposite rays.
 Like points, segments and              B
rays are collinear if they       C
lie on the same line. So,
any two opposite rays are
collinear. Segments, rays    A
and lines are coplanar if            Line   l or AB
they lie on the same
plane.
Ex. 2: Drawing lines, segments
and rays
   Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.
Draw J, K and L
K
Then draw JK

J
L
Ex. 2: Drawing lines, segments
and rays
   Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.

K
Draw KL

J
L
Ex. 2: Drawing lines, segments
and rays
   Draw three noncollinear points J, K, and L.
Then draw JK, KL and LJ.

K
Draw LJ

J
L
Ex. 3: Drawing Opposite Rays
   Draw two lines. Label
points on the lines and
name two pairs of           M
opposite rays.                      Q

Solution: Points M, N, and          X
X are collinear and X is
between M and N. So XM
and XN are opposite rays.   P       N
Ex. 3: Drawing Opposite Rays
   Draw two lines. Label
points on the lines and
name two pairs of           M
opposite rays.                      Q

Solution: Points P, Q, and X        X
are collinear and X is
between P and Q. So XP
and XQ are opposite rays.   P       N
Goal 2: Sketching Intersections of
Lines and Planes
 Two or more geometric 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.
 Activity: p. 12 – Modeling intersections.
– Use two index cards. Label them as shown
and cut slots along each card.
 Complete the exercise and place the completed
questions in your lab section labeling this Lab 1.2.
Ex. 4: Sketching intersections
    Sketch the figure
described.
a.   A line that intersects a
plane in one point
    Draw a plane and a
line.
    Emphasize the point
where they meet.
    Dashes indicate where
the line is hidden by
the plane
Ex. 4: Sketching intersections
    Sketch the figure
described.
b.   Two planes that
intersect in a line
    Draw two planes.
    Emphasize the line
where they meet.
    Dashes indicate where
one plane is hidden by
the other plane.
Union
   An angle is the union ( ) of two
noncollinear rays with a common
endpoint.
In geometric notation:

AB     AC  CAB

B        Union means
A                        combining two
sets into a
larger set
C
Intersection
   The intersection symbol ( ) means the
objects that figures have in common.

For example:   ABC    BC  BC

Note: Segment BC is
A              common with itself
and the triangle.

B                          C
Now for some practice…

Assignment . .
 Pages   7-8 # 1-13 all

```
To top