The document provides definitions and examples related to geometry, specifically focusing on concepts like congruence, betweenness of points, midpoints, and distance formulas. It explains that congruent figures have the same size and shape, and outlines how to determine segment lengths and midpoints. Additionally, an example is given involving algebraic expressions to find values related to segments and their midpoints.

1. Segments
Betweeness of Points, Midpoints, Bisectors,
and Constructions
FoundationsofGeometry

2. Definition Congruent :
● figures the same in size and shape
● segments with the same length

3. Notation
If the length of segment CD is the same as
the length of segment AB, then:
● AB = CD ⇒distance from A to B equals
distance from C to D
● ⇒segment AB is congruent to
segment CD
A
B
`
C
D

4. Construction

5. Definition Betweeness of Points:

6. Example
If AB = 24, AG = 2x and GB = 5x + 3,
find x and find AG and GB.
A G B

7. Definition Midpoint:
If M is between A & B and AM = MB,
then M is the midpoint of segment AB
A BM

8. Formula

9. Example

10. Example

11. Formula Distance Between Points:

12. Example

13. Example

14. Definition

15. Construction