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Aim:. What are the undefined terms ?. Do Now: What is a point? What is a line? 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 . Point:. . A(2, 6). Y. X.
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Aim:
What are the undefined terms?
- Do Now:
- What is a point?
- What is a line?
- 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.
Geometry Leeson: Undefined Terms, Lines, Line Segments
Point:
. A(2, 6)
Y
X
A point indicates a position or location in space.
. P
Points are named using capital letters and/or coordinates.
Geometry Leeson: Undefined Terms, Lines, Line Segments
Line:
Ex: Curved line
Ex: Straight line
- Naming a Line:
- Two points on the line:
- Single lowercase letter
A
B
C
m
A line is an infinite set of adjacent points.
Geometry Leeson: Undefined Terms, Lines, Line Segments
Plane:
- Naming a Plane:
- Three points on the plane:
- Single uppercase letter:
B •
C•
Plane ABC
A •
Plane R
R
A plane is a set of points that forms a completely flat surface.
Geometry Leeson: Undefined Terms, Lines, Line Segments
Def: Collinear Points:
E
A
B
C
D
A collinear set of points is a set of points all of which lie on the same straight line.
- Points A, B, C and D are collinear.
- Points A, E and C are notcollinear.
Geometry Leeson: Undefined Terms, Lines, Line Segments
Def: Line Segment:
A
B
Naming a Line Segment:
Use the names of the endpoints.
A
B
“Line segment”
is part of “Line”
A line segment is the set of two points on a line called endpoints, and all points on the line between the endpoints.
Geometry Leeson: Undefined Terms, Lines, Line Segments
Measure of Line Segments:
To indicate the “measure” of a line segment, use the name of the line segment without the line above the name.
Ex:
= “measure of line segment”
Ex: The perimeter of
is 58 cm.
If AB = x - 4, BC = 2x + 8, and CA= x – 2, what is BC?
The measure of a line segment is the length of the line segment.
Ans. BC=36 cm
Geometry Leeson: Undefined Terms, Lines, Line Segments
Def: Congruent Line Segments:
Ex:
A
B
If
C
D
Congruent line segments are segments that are equal in measure.
Then AB = CD
Ans. CD = 29, AB = 29
Geometry Leeson: Undefined Terms, Lines, Line Segments
Def: Midpoint
M
A
B
1)
3)
5)
2)
4)
6)
The midpoint of a line segment divides the line segment into two congruent segments.
Geometry Leeson: Undefined Terms, Lines, Line Segments
Def: Line Bisector
Q
A
B
M
P
1)
1)
2)
The bisector of a line segment is a line that intersects the line segment at its midpoint.
X
Geometry Leeson: Undefined Terms, Lines, Line Segments
Addition and Subtraction of Line Segments:
S
P
R
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
Simple 2-Column Proof
B
P
F
E
A
Given
Definition of Line Bisector
Definition of Midpoint
Geometry Leeson: Undefined Terms, Lines, Line Segments
