Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts in geometry do not have precise definitions but, we understand their meanings intuitively. We say these concepts are undefined . What are the undefined terms?
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Geometry Leeson: Undefined Terms, Lines, Line Segments 1 Aim: Do Now: 1)What is a point? 2)What is a line? 3)What is a plane? The most fundamental concepts.
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Geometry Leeson: Undefined Terms, Lines, Line Segments
1
Aim:
Do Now:
1) What is a point?
2) What is a line?
3) What is a plane?
The most fundamental concepts in geometry do not have precise definitions but, we understand their meanings intuitively. We say these concepts are undefined.
What are the undefined terms?
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Geometry Leeson: Undefined Terms, Lines, Line Segments
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A point indicates a position or location in space.
. P
X
Y
. A(2, 6)
Point:
Points are named using capital letters and/or coordinates.
Geometry Leeson: Undefined Terms, Lines, Line Segments
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A line is an infinite set of adjacent points.Line:
Ex: Curved line
Ex: Straight line
Naming a Line:
a) Two points on the line:
b) Single lowercase letter
, , , , ...AB AC BA BC etc�������������������������������������������������������������������������������������������� �������
A B C
m
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Plane: A plane is a set of points that forms a completely flat surface.
Naming a Plane:
a) Three points on the plane:
b) Single uppercase letter:
A •C•
B •
Plane ABC
R
Plane R
Intersections?
• Lines intersect at a point
• Planes intersect at a line
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Def: Collinear Points:A collinear set of points is a set of points all of which lie on the same straight line.
A B C D
E
•Points A, B, C and D are collinear.
•Points A, E and C are not collinear.
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Def: Line Segment:
Naming a Line Segment:
Use the names of the endpoints.
A B
“Line segment” AB is part of “Line” AB�������������� �
A line segment is the set of two points on a line called endpoints, and all points on the line between the endpoints.
A B
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Measure of Line Segments:
The measure of a line segment is the length of the line segment.
To indicate the “measure” of a line segment, use the name of the line segment without the line above the name.
ABEx: = “measure of line segment”
AB
Ex: The perimeter of ABC is 58 cm.If AB = x - 4, BC = 2x + 8, and CA= x – 2, what is BC? Ans. BC=36 cm
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Def: Congruent Line Segments:
Congruent line segments are segments that are equal in measure.
Then AB = CD
E x : I f A B C D , 9 7A B x a n d 4 1 3C D x , w h a t is C D ? A B ?
Ans. CD = 29, AB = 29
Ex: A
C D
B If AB CD
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Def: Midpoint The midpoint of a line segment divides the line segment into two congruent segments.
A BM
If M is the midpoint of AB, then: 1)
3)
5)
2)
4)
6)
AM MB AM MB
1
2AM AB
1
2MB AB
2AB AM 2AB MB
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Def: Line Bisector The bisector of a line segment is a line that intersects the line segment at its midpoint.
A BM
P
QPMQ�������������� �
is a bisector of AB
If PMQ�������������� � bisects AB at M, then: M is midpoint of AB 1)1)
XM is midpoint of PQ�������������� �? 2)
If PMQ�������������� � intersects AB at its midpoint M, then:
PMQ�������������� �
is a bisector of AB
Geometry Leeson: Undefined Terms, Lines, Line Segments
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Addition and Subtraction of Line Segments:
R
P
S
__RS RP
-__RP RS
PS
PS
RS RP PS
RP RS PS
-__PS RS RPPS RS RP
If several line segments belong to the same line, we can write addition and subtraction expressions using the names of these segments.
Geometry Leeson: Undefined Terms, Lines, Line Segments