Download Chapter 1 - Humble ISD

Chapter 1
Understanding
Points, Lines,
and Planes
Geometry
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The branch of mathematics that studies the
shapes of objects and their sizes, properties
and relationships, and spatial reasoning.
Geo - “earth”
metry - “measure”
–
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Geometry literally means earth measure
We will study the logical structures of
geometry and its relationships to algebra,
probability and triogonometry.
Terms MUST KNOW!
*Point – names a
location
Has no size.
Use capital letters
EX: P, Point P, Pt P,
Not: •P (u do not
need the • to name a
pt)
*Line – straight
path that never
ends **
Symbol
to name: AB
BA or line l
*Plane – flat
surface that
extends forever
To name use the
Script capital letter
or 3 points not on the
same line.
EX: P or ABC
•P
•Q
A
B
P
l
B
C
A
Terms Continued….
Segment – part of a
line consisting of 2
pts and all pts in
between **
Symbol
CD or DC
not CD (must have
C
D
segment above letters)
Endpoint – pt at one
end of a segment or
the starting pt of a ray
C
or
D
Ray – part of a line
Symbol
that starts at an endpt
& extends forever in 1 AB or CD
direction **
not BA (the endpt
must be the first pt listed)
look at the above
pictures points C
and D are endpts
A
B
D
C
Terms Continued…
Opposite Ray – 2
rays with a
common endpt
that form a line
BA
&
BC
A
B
C
Collinear
Pts on the same
line
3 non-collinear pts
determine a plane
Coplanar
Pts on the same
plane
If 2 pts are in a
plane, then the line
containing them is
in the plane
* The most basic figures, points, lines, and
planes are “undefined terms” in geometry.
This means they cannot be defined using
other figures.
** 2 letters without a symbol refers to distance.
you must use the correct symbol to represent
either a line, segment, or ray!!
ONLY HONORS NEEDS TO WRITE
THIS SLIDE!
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The Geometry we are familiar with and the kind we will
study is called Euclidean geometry, named after the
Greek mathematician, Euclid.
Other geometries, called non-Euclidean
– Spherical Geometry – geometry of the sphere. More
suited to our earth. Planes are the surfaces of a
sphere and all lines are circles on the sphere
– Hyperbolic Geometry – geometry on a circular plane
– Coordinate Geometry – (analytic geometry) uses the
coordinate system (x,y) to study properties of lines,
segments, etc.
Examples
1. Name the two planes. M & N
2. What is the intersection of the
two planes? AB
3. Which plane contains points G,
E and D? M
4. Which plane contains point H? N
5. What points are not in both
planes? G, E, D, C, H, W
6. Name a point not in plane N. G
7. Point F is the intersection of _
____
AB and ______.
CH
Examples
True or False
8. B, E, and D are True
coplanar
9. G, A, and F are False
collinear
10. H and E determine a True
line
11. C & H determine
False
plane N
12. ray AF and ray FB False
are opposite rays
13. Line AB and Plane M
have exactly 3 points of False
intersection.
Optical Illusions

Your eyes see images and send them to your
brain to interpret, but sometimes the brain
can be tricked and your spatial reasoning is
tested.
Optical Illusion Examples
Are the petals moving?
you will probably find it hard to believe that
squares A and B are actually the same
shade of gray
Honors Only!!
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Slope formula y2-y1 = m
x2-x1
y = mx + b
y – y1 = m(x – x1)
Parallel lines have SAME slope DIFF y- intercepts
Perpendicular lines’ slopes are opposite reciprocals
example : 3 and -1/3
Oblique lines have DIFFERENT slopes, not opposite
reciprocals