Segments and DistancesRays and Angles

One-Dimensional Euclidean Geometry

Recap of Undefined TermsSPACE 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.

A

l

B C

line l or l

line BC or line CB

BC or CB

From the undefined terms...

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 CBBC or CB

From the undefined terms...

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.

A RAY is a LINE SEGMENT that extends in ONLY ONE DIRECTION.

D E

ray DE or DED E

D E

ray ED or ED

ED

line DE or line ED

DE or ED

Euclid’s First Rules on Lines

ALL LINES are straight.ALL LINES and SUBSETS OF LINES are

sets of POINTS. Every SEGMENT corresponds to a unique

POSITIVE NUMBER called DISTANCE.

5 km5,000 m500 dam

A B

Euclid’s First Rules on Lines

The INTERSECTION or the place where TWO DIFFERENT LINES meet is either ONE POINT or EVERY POINT in the line.

A

BC

Exercise One

.1.Name five lines.

2.Name five line segments.

3.Name five rays.

1-D Euclidean Geometry

AB

C

D

O

F

E

G

H

I

J K

L

From the undefined terms...

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 POINTSlie on the same line.

From this we candefine ANGLES.

A

B

C

Constructing Angles

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

B

C

angle ABC or ABC

angle B or Bangle CBA or

CBA

Types of Angles

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

Types of Angles

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

Types of Angles

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

.A

B

C

D

O

F

E

G

H

I

J K

L

Exercise Two

Name four of each type of angle:•acute•right•obtuse

1-D Euclidean Geometry

Quiz on One-Dimensional Euclidean GeometryFive Items True or False (45 seconds)Four Items Deductive Reasoning (20 seconds each)

Part One. True or False

1. All lines are STRAIGHT.2. TWO NON-COLLINEAR POINTS

make up an angle.3. ALL LINES and SUBSETS OF

LINES are made up of points.4. ACUTE ANGLES look more like

open books.5. A ray is a line segment that extends

in ONLY ONE DIRECTION.

Part Two. Deductive Reasoning

6. Name all the ACUTE ANGLES formed by the intersection of these lines.

7. What are the line segments comprising the ANGLE EAD?

A

B

C

ED

Part Two. Deductive Reasoning

8. If the distance AB is 5 meters, and the distance BC is 20 decimeters, how many centimeters does the distance AC have, given that A-B-C?

9. Draw angle OMG. Then, draw a line segment MP such that point P is inside angle OMG.