1.3: Segments, Rays, and Distance

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Presentation transcript:

1.3: Segments, Rays, and Distance

Line segment: two points on a line and all points in between them 2 points are called endpoints Ray: a figure with one endpoint and goes on forever in the opposite direction Opposite Rays: 2 rays that make up a line

Length: distance between 2 points Subtract 2 coordinates on a number line to find length Greater minus smaller

Postulate 1: Ruler Postulate 1.) 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 2.) Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates

In Human terms Basically, you can set any two points as 0 and 1 and that will now be your scale And distance will always be positive

Postulate 2: Segment Addition Postulate If B is between A and C, then AB + BC = AC Ex: B is between A and C with AB = x and BC = x + 8, and AC = 32. Find the length of each.

Congruent: objects that have the same size and shape Congruent Segments: Segments that have equal lengths Notation: Equal lengths: DE = FG Congruent: Used interchangeably

Midpoint of a segment: the point that divides the segment into 2 congruent segments AM = MB or M is the midpoint of segment AB

Bisector of a segment A line, segment, ray, or plane that intersects the segment at its midpoint Draw picture

Homework Pg 15: 2-46 even