1.2 Points, Lines, and Planes the 3 undefined terms of Geometry Geometry.
1.2 Points, Lines and Planes
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1.2 Points, Lines and Planes
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1.2 Points, Lines and Planes. undefined terms. There are three __________ ____________ in geometry. The following are not definitions, they are descriptions. point. 1 A ______________ is the simplest figure studied in geometry. It doesn’t have any size. It is represented by a dot. A. - PowerPoint PPT Presentation
Transcript of 1.2 Points, Lines and Planes
1.2 Points,
Lines and Planes
There are three __________ ____________ in geometry.
The following are not definitions, they are descriptions.
undefined terms
•1 A ______________ is the simplest figure studied in geometry. It doesn’t have any size. It is represented by a dot.
point
All geometric figures consist of points. Below are points A, B and C. We name points
with capital letters.A
BC
•2 A ________ extends in two
directions without ending.
It has no thickness.
line
A line is referred to by a single lower case letter (line l ) or using two points on the line (AB or BA).
B
A
l
•3 A __________ is suggested by a floor, wall or table top. However, it exists without ending and has no thickness.
plane
•We use a parallelogram to represent a plane. We label a plane with a capital letter.
M N
Plane M and Plane N.
•We use the three undefined terms to define other concepts.
DCBA
•_________ _________ are points that lie on the same line.
Points A, B, C are collinear. Points A, B and D are noncollinear.
Collinear points
•___________ _________ points are points that lie on the same plane.
• M, N, P, R are coplanar.• M, N, P, Q are noncoplanar.
MN
R
P
Q
Coplanar points
The ____________of two figures is the set of points that are in
both figures.
intersection
Pt
m
Lines m and t intersect at point W.
W
Point P is on line t.
•k and P are in M.•M contains k and P•j intersects M at P.•P is the intersection of j and M.
Pk
M
j
M
N
Y
X
Planes M and N intesect in line XY.
•Ex 1. Using the figure given, list three sets of collinear points.
•Ex 2. List a set of noncollinear points.
AB
C
D
EF
G
A, B, C
F, E, B
A, E, G
A, E, CF, E, C orA, B, D or
M
O
T
WR
S
X
Y
Ex 3. Copy this figure into your notebooks and then answer the T/F questions.
• A) Line XY intersects M at point O.
• B) Plane M intersects line XY in more than one point.
• C) T, O, and R are collinear.• D) X, O, and Y are collinear.• E) R, O, S, and W are coplanar.• F) R, S, T, and X are coplanar.• G) R, X, O and Y are coplanar.
T
F
F
T
T
F
T
• Ex 4. Name a fourth point that is in the same plane as the given points.
• a) A, B, C• b) D, C, H• c) B, E, F• d) D, B, F
D
E
A
H
C
G
F
B
•The plane that contains the top of the box• can be called plane ABCD. (Go around in order)
D
GAH
A. Are there more than 4 points in plane ABCD?
B. Are there any points in line CG besides C and G?
C. Name the intersection of planes ABFE and BCGF.
D. Name two planes that do not intersect.
Ex 5.
Yes!! Yes!
!BFABBBBBBBBBBBBB B
ABCD and EFGH
ADHE and BCGF ABFE and DCGH
____________________ consists of points A and C and all points that
are between A and C.
•A and C are called the _____________ of segment AC.
Segment AC
endpoints
A C
AC or CA
__________________ consists of the initial point A and all the
points on line AC that lie on the same side of A as point C.
Ray AC
Name the endpoint first.
A C AC not CABBBBBBBBBBBBBBBBBBBBBBBBBBBB
R S T
Ex 6. Write 3 times when the hands of the clock are opposite rays.
SR and ST are called opposite rays if S is
between R and T
BBBBBBBBBBBBBBBBBBBBBBBBBBBB
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