1.3 Segments, Rays, and Distance

• Segment – Is the part of a line consisting of two endpoints & all the points between them.– Notation: 2 capital letters with a line over

them.

– Ex:– No arrows on the end of a line. – Reads: Line segment (or segment) AB

A B

AB

• Ray – Is the part of a line consisting of one endpoint & all the points of the line on one side of the endpoint.– Notation: 2 capital letters with a line with an

arrow on one end of it. Endpoint always comes first.

– Ex: – Reads: Ray AB– The ray continues on past B indefinitely

A B

AB

AB

• Opposite Rays – Are two collinear rays with the same endpoint. – Opposite rays always form a line.

– Ex:

Same Line

Q R S

RQ & RS

Endpoints

Examples of Opposite Rays

Ex.1: Naming segments and rays.

• Name 3 segments:– LP– PQ– LQ

• Name 4 rays:– LQ– QL– PL– LP– PQ

L P Q

Are LP and PL opposite rays??

No, not the same endpoints

Group Work

• Name the following line.

• Name a segment.

• Name a ray.

X

Y

ZXY or YZ or ZX

XY or YZ or XZ

XY or YZ or ZX or YX

Number Lines

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

JK M

Number Lines

• In the diagram, point J is paired with 8

• We say 8 is the coordinate of point J.

JK M

Length of MJ

• When I write MJ = “The length MJ”

• It is the distance between point M and point J.

JK M

I want a real number as the

answer

Length of MJ

• You can find the length of a segment by subtracting the coordinates of its endpoints

JK M

• MJ = 8 – 5 = 3 • MJ = 5 - 8 = - 3

Either way as long as you take the absolute value of the answer.

Postulates and Axioms

• Statements that are accepted without proof– They are true and always will be true– They are used in helping to prove further

Geometry problems, theorems…..

• Memorize all of them– Unless it has a name (i.e. “Ruler Postulate”)– Not “Postulate 6”

• named different in every text book

Ruler Postulate

• The points on a line can be matched, one-to-one, with the set of real numbers. The real number that corresponds to a point is the coordinate of the point. (matching points up with a ruler)

• The distance, AB, between two points, A and B, on a line is equal to the absolute value of the difference between the coordinates of A and B. (absolute value on a number line)

Remote time

A- Sometimes B – Always C - Never

• The length of a segment is ___________ negative.

• If point S is between points R and V, then S ____________ lies on RV.

A- Sometimes B – Always C - Never

• A coordinate can _____________ be paired with a point on a number line.

A- Sometimes B – Always C - Never

Segment Addition Postulate

• Student demonstration

• If B is between A and C, then AB + BC = AC.

A

C

B

Example 1

• If B is between A and C, with AB = x, BC=x+6 and AC =24. Find (a) the value of x and (b) the length of BC. (pg. 13)

A

C

B

Write out the problem based on the segments, then substitute in the info

Congruent

• In Geometry, two objects that have– The same size and– The same shape

are called congruent.

What are some objects in the classroom that are congruent?

Congruent __________

• Segments (1.3)

• Angles(1.4)

• Triangles(ch.4)

• Circles(ch.9)

• Arcs(ch.9)

Congruent Segments

• Have equal lengths

• To say that DE and FG have equal lengthsDE = FG

• To say that DE and FG are congruentDE FG

2 ways to say the exact same thing

Midpoint of a segment

• Based on the diagram, what does this mean?

• The point that divides the segment into two congruent segments.

A

B

P

3

3

Bisector of a segment

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

A

B

P

3

3

Something that is going to cut

directly through the midpoint

Remote time

• A bisector of a segment is ____________ a line.

A- Sometimes B – Always C - Never

• A ray _______ has a midpoint.

A- Sometimes B – Always C - Never

• Congruent segments ________ have equal lengths.

A- Sometimes B – Always C - Never

• AB and BA _______ denote the same ray.

A- Sometimes B – Always C - Never

Ch. 1 Quiz

Know the following…

1. Definition of equidistant

2. Real world example of points, lines, planes

3. Types of intersections

4. Points, lines, planes1. Characteristics

2. Mathmatical notation