Warm – up True / false : If false, explain why Collinear points are coplanar Planes have edges Two planes intersect in a line segment Two intersecting lines meet in exactly one point Line XY can be denoted as XY or YX. A line has one endpoint

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 AB A B

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 AB A B B A

Opposite Rays – Are two collinear rays with the same endpoint. Same Line Opposite Rays – Are two collinear rays with the same endpoint. Opposite rays always form a line. Ex: RQ & RS S Q R Endpoints

Group Work Name the following line. Name a segment. XY or YZ or ZX Name a ray. XY or YZ or ZX Z XY or YZ or XZ Y Are XY and YX opposite rays?? No, not the same endpoints XY or YZ or ZX or YX X

Number Lines On a number line every point (LETTER) is paired with a coordinate (NUMBER) What is the coordinate of each letter? K M J

What is the Length of MJ? FIND MJ When I write MJ it means “The length MJ” It is the distance between point M and point J. Length/distance is always positive!! FIND MJ K M J

Questions 1 -9 -

Congruent  In Geometry, two objects that have are called congruent. The same size and The same shape are called congruent. What are some objects in the classroom that are congruent? Congruent markings for segments and angles

Congruent Segments Have equal lengths To say that DE and FG have equal lengths DE = FG To say that DE and FG are congruent DE  FG 2 ways to say the exact same thing

Questions 10, 11 15 – 20, 12

Definition: 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 What marking do we use to show congruent segments?

Definition: Bisector of a segment A line, segment, ray or plane that intersects the segment at its midpoint. A B P 3 Something that is going to cut directly through the midpoint

Marking diagram with given information P. 15 – problems 5 – 18 P. 16 – 33 - 36

Postulates Statements that are accepted without proof Learn them! They are true and always will be true They are used in helping to prove further Geometry problems, theorems….. Learn them! Unless it has a name (i.e. “Ruler Postulate”) Not “Postulate 6” named different in every text book

Segment Addition Postulate Student demonstration If B is between A and C, then AB + BC = AC. A C B

Example 1 Use the rule for segment addition postulate to set up an equation A C B Write out the problem based on the segments, then substitute in the info

Example 2 Use the rule for midpoint to set up an equation B is the midpoint of segment AC A C B

A- Sometimes B – Always C - Never A bisector of a segment is ____________ a line. A ray _______ has a midpoint. Congruent segments ________ have equal lengths. AB and BA _______ denote the same ray.

Ch. 1 Quiz Know the following… Definition of equidistant Real world example of points, lines, planes Types of intersections (drawings) Points, lines, planes Characteristics Mathematical notation