HONORS GEOMETRY

1.3 Definitions and Postulates

Lesson Focus

We will see how numbers can be related to points on a line. This will show the ideas of distance, length , and congruence.

DefinitionsTERM DEFINITION GRAPHIC SYMBOL

LINE SEGMENT

Part of a line that is bounded by two distinct end points, and contains every point on the line between its end points

LENGTH The distance between two endpoints of a line

n/a The length of is denoted by AB

RAY A line that extends infinitely from an endpoint

OPPOSITE RAY Rays with the same endpoint that extend in opposite directions

and are opposite rays

Guided Practice

1. Give 3 names for thisline. _______________

2. Name 2 line segments:_____________________

3. Name 2 rays:_________________

4. Name opposite rays: ______________

Definitions

TERM DEFINTION GRAPHIC SYMBOL

CONGRUENT SEGMENTS

Two segments that have equal length

MIDPOINT OF A SEGMENT

A point that divides the segment into two congruent segments

P is the midpoint of

SEGMENT BISECTOR

A line, segment, ray, or plane that intersects the segment at its midpoint

Line l is the bisector of . and plane X also bisect .

Definitions

Point P is between points A and B. This means P must like on .

Postulates/Axioms are statements that are accepted without proof.

Postulate

Postulate 2: Segment Addition Postulate

If B is between A and C, then

AB + BC = AC

Guided Practice

B is between A and C with AB = x. BC = x + 6 and AC = 24.

1. Find the value of x. 2. Find BC.

Guided Practice

T is the midpoint of . If LT = 4x +3 and MT= 2x + 9:

1. Evaluate for x. 2. Evaluate LT.

Guided Practice

3. Evaluate MT.

4. Evaluate LM.

NUMBER LINE

On a number line, every point is paired with a number and every number is paired with a point.

RULER POSTULATE

The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1.

Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of the coordinates.

Finding the Length

The distance between two points can be found by subtracting the coordinates of its endpoints:

1. CG =

2. HK =

Finding the Length

Guided Practice