High School Geometry: betweeness of points, congruence, construct congruent segments and segment bisectors, midpoints, and distance between points

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