1. Geometric
Basics

2. Points Points do not have actual size. How to Sketch: Using dots
How to label:
Use capital letters
Never name two points with the same letter in the same sketch. A B A

3. Lines B C n A Extend indefinitely and have no thickness or width.
How to sketch : using arrows at both ends.
How to name: 2 ways
(1) small script letter
line n
(2) any two points on the line
Never name a line using three points n A B C

4. Collinear Points
Lie on the same line. (The line does not have to be visible). A B C
Non collinear C A
Collinear B

5. Planes Flat surface that extends indefinitely in all directions.
How to sketch: Use a parallelogram (four sided figure)
How to name: 2 ways
(1) Capital script letter
Plane M
(2) Any 3 non collinear points in the plane
Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C
Horizontal Plane
Vertical Plane
Other

6. Different planes in a figure:B
Plane ABCD
Plane EFGH
Plane BCGF
Plane ADHE
Plane ABFE
Plane CDHG
Etc. D C E F H G

7. Other planes in the same figure:
Any three non collinear points determine a plane!
Plane AFGD
Plane ACGE
Plane ACH
Plane AGF
Plane BDG
Etc.

8. Coplanar Objects
Coplanar objects (points, lines, etc.) lie on the same plane. The plane does not have to be visible.
Are the following points coplanar?
A, B, C ?
Yes
A, B, C, F ? No
H, G, F, E ?
Yes
E, H, C, B ?
Yes
A, G, F ?
Yes
C, B, F, H ? No

9. Segment
Definition:
Part of a line that consists of two points called the endpoints and all points between them.
How to sketch:
How to name:
AB (without a symbol) means the length of the segment or the distance between points A and B.

10. Congruent Segments Congruent segments can be marked with dashes.
Definition:
Segments with equal lengths. (congruent symbol: )
Congruent segments can be marked with dashes.

11. Ray Definition: RA : RA and all points Y such that
A is between R and Y.
How to sketch:
How to name:
( the symbol RA is read as “ray RA” )

12. Opposite Rays Definition:
If A is between X and Y, AX and AY are opposite rays.
( Opposite rays must have the same “endpoint” )
opposite rays
not opposite rays

13. Intersection of Figures
The intersection of two figures is the set of points that are common in both figures.
The intersection of two lines is a point. m P n
Line m and line n intersect at point P.

14. 3 Possibilities of Intersection of a Line and a Plane
(1) Line passes through plane – intersection is a point.
(2) Line lies on the plane - intersection is a line.
(3) Line is parallel to the plane - no common points.

15. Intersection of Two Planes is a Line.B P A R
Plane P and Plane R intersect at the line

16. Segment Bisectors Definition:
Any segment, line or plane that divides a segment into two congruent parts is called segment bisector.

17. Between AX + XB = AB AX + XB > AB
Definition: X is between A and B if AX + XB = AB.
AX + XB = AB
AX + XB > AB

18. The Segment Addition Postulate
If C is between A and B, then AC + CB = AB.
Example:
If AC = x , CB = 2x and AB = 12, then, find x, AC and CB. 2x x 12
Step 1: Draw a figure
Step 2: Label fig. with given info.
AC + CB = AB
x x = 12
3x = 12
x = 4
Step 3: Write an equation
x = 4
AC = 4
CB = 8
Step 4: Solve and find all the answers

19. You Try It! Complete Practice Problems and check your answers with one another.