1. What are the undefined terms?
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

2. Geometry Leeson: Undefined Terms, Lines, Line Segments

3. . P . A(2, 6) A point indicates a position or location in space.X Y
. A(2, 6)
Points are named using capital letters and/or coordinates.
Geometry Leeson: Undefined Terms, Lines, Line Segments

4. A line is an infinite set of adjacent points.
Ex: Curved line
Ex: Straight line
Naming a Line:
Two points on the line:
Single lowercase letter A B C m
Geometry Leeson: Undefined Terms, Lines, Line Segments

6. A plane is a set of points that forms a completely flat surface.
Naming a Plane:
Three points on the plane:
Single uppercase letter:
A • C•
B •
Plane ABC R
Plane R
Geometry Leeson: Undefined Terms, Lines, Line Segments

7. Intersections?
Lines intersect at a point
Planes intersect at a line

8. 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

9. Use the names of the endpoints.
Def: Line Segment: A B
A line segment is the set of two points on a line called endpoints, and all points on the line between the endpoints.
Naming a Line Segment:
Use the names of the endpoints. A B
“Line segment”
is part of “Line”
Geometry Leeson: Undefined Terms, Lines, Line Segments

10. 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.
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?
Ans. BC=36 cm
Geometry Leeson: Undefined Terms, Lines, Line Segments

11. Def: Congruent Line Segments:
Congruent line segments are segments that are equal in measure.
Ex: A C D B If
Then AB = CD
Ans. CD = 29, AB = 29
Geometry Leeson: Undefined Terms, Lines, Line Segments

12. Def: Midpoint
The midpoint of a line segment divides the line segment into two congruent segments. A B M 1) 3) 5) 2) 4) 6)
Geometry Leeson: Undefined Terms, Lines, Line Segments

13. X A B 1)  2) Def: Line Bisector
The bisector of a line segment is a line that intersects the line segment at its midpoint. A B M P Q 1)  2) X
Geometry Leeson: Undefined Terms, Lines, Line Segments

14. Addition and Subtraction of Line Segments:
If several line segments belong to the same line, we can write addition and subtraction expressions using the names of these segments. R P S
Geometry Leeson: Undefined Terms, Lines, Line Segments

15. Simple 2-Column Proof B P F E A Given Definition of Line Bisector
Definition of Midpoint
Geometry Leeson: Undefined Terms, Lines, Line Segments