A presentation for students regarding segments, rays, and angles. Also involves a 9-item quiz and exercises, as well as demonstrative techniques of "stretching" points to transform them to lines, rays, segments, and angles.

1. One-Dimensional Euclidean Geometry

2. SPACE is the set of ALL POINTS.

A POINT is an exact place in space. It is

denoted by a dot, having no measurement
nor dimension. POINTS are named using
capital letters.
A LINE is a stream of POINTS that doesn’t

end, and extends in both directions. LINES
are named by a small letter or any two
POINTS CONTAINED in the LINE.

3. l
A
line l or l
B C
line BC or line CB
BC or CB

4. We can define a segment. A LINE SEGMENT

is a SUBSET/PORTION of a LINE that
includes TWO POINTS and all the POINTS in
BETWEEN.
B C
segment BC or segment CB
BC or CB

5. We can define a ray. A RAY is a

SUBSET/PORTION of a LINE that includes
one point called the ENDPOINT and all the
POINTS on one side of the ENDPOINT.
D E
A RAY is a LINE SEGMENT that extends in

ONLY ONE DIRECTION.

6. D E
ray DE or DE
D E
ray ED or ED
D E
line DE or line ED
DE or ED

7. ALL LINES are straight.

ALL LINES and SUBSETS OF LINES are sets

of POINTS.
Every SEGMENT corresponds to a unique

POSITIVE NUMBER called DISTANCE.
B
A 5 km
5,000 m
500 dam

8. The INTERSECTION or the place where TWO

DIFFERENT LINES meet is either ONE
POINT or EVERY POINT in the line.
A
B
C

9. 1-D Euclidean Geometry
Exercise One
1. Name five . G
A
lines. B
2. Name five C
line D H L
segments. E O
I
3. Name five F
rays. J K

10. We can also determine a set of non-collinear

points. NON-COLLINEAR POINTS are three
or more points that are not contained on the
same time.
COLLINEAR POINTS

lie on the same line. A
From this we can

define ANGLES. B
C

11. TWO NON-COLLINEAR RAYS that share the

SAME ENDPOINT form an ANGLE. The
POINT where the rays intersect is called the
VERTEX of the angle. The RAYS are called
the SIDES of the angle.
A
angle ABC or ABC B
angle CBA or CBA C
angle B or B

12. An ACUTE ANGLE is one measuring LESS

THAN 90°. It looks more like a closed book.

13. A RIGHT ANGLE is one measuring EXACTLY

90°. It looks more like a corner.

14. An OBTUSE ANGLE is one measuring MORE

THAN 90°. It looks more like an open book.

15. 1-D Euclidean Geometry
Exercise Two
Name four . G
A
of each B
type of C
angle: D H L
E O
•acute I
F
•right
J K
•obtuse

16. Five Items True or False (45 seconds)
Four Items Deductive Reasoning (20 seconds each)

17. All lines are STRAIGHT.
1.
TWO NON-COLLINEAR POINTS make up
2.
an angle.
ALL LINES and SUBSETS OF LINES are
3.
made up of points.
ACUTE ANGLES look more like open books.
4.
A ray is a line segment that extends in ONLY
5.
ONE DIRECTION.

18. Name all the ACUTE ANGLES formed by
6.
the intersection of these lines.
E
D
A
B
C
What are the line segments comprising the
7.
ANGLE EAD?

19. If the distance AB is 5 meters, and the
8.
distance BC is 20 decimeters, how many
centimeters does the distance AC have,
given that A-B-C?
Draw angle OMG. Then, draw a line segment
9.
MP such that point P is inside angle OMG.