Remember A segment is the part of a line between two points.  Remember A segment is the part of a line between two points.  You name a segment by putting a bar over the names of the endpoints.

Ruler postulate . You can assign a number. (called the coordinate) to Ruler postulate  You can assign a number (called the coordinate) to any point on a line.  Basically you can turn any line into a number line.

Distance between 2 points The notation AB (with nothing on top of the letters) means the distance between A and B.  If the coordinate of A is a and the coordinate of B is b, then AB = | a – b |. Here AB = 3

Find these distances: MD WG TY YB GT DW

Find these distances: MD = | 6 – 1 | = 5 WG = | 8 – -6 | = 14 TY = | -9 – -2 | = 7 YB = | -6 – -1 | = 5 GT = | -10 – -9 | = 1 DW = | 6 – 8 | = 2

YES, you can just count. MD = 5 WG = 14 TY = 7 YB = 5 GT = 1 DW = 2

Between B is between X and Y. if and only if . X, B, and Y are all Between B is between X and Y if and only if  X, B, and Y are all collinear  XB + BY = XY

Between B is between X and Y. if and only if . X, B, and Y are all Between B is between X and Y if and only if  X, B, and Y are all collinear  XB + BY = XY

In this picture B is between A and C, but D is NOT BETWEEN A and C (nor are E and F)

Some books call this the definition of between Some books call this the definition of between. Your book calls it the segment addition postulate. The name doesn’t matter, but you do need to know the parts add up to the whole.

Midpoint. __ M is the midpoint of AB if and only if  Midpoint __ M is the midpoint of AB if and only if  M is between A and B  AM = MB

Congruent (This is just about the most important term in geometry. )  Congruent (This is just about the most important term in geometry.)  Same size and shape  Symbol   Segments are congruent if they have the same measures.

In pictures we show segments are congruent by marking them with slashes.

Which segments are congruent here?

Which segments are congruent here? AB and ED BC and EF AC and DF

NOTE: Unless segments are marked or you are told in directions, you can’t just assume they are congruent.

KNOW (symbols and meaning) … distance between midpoint congruent