1.3 SEGMENTS AND THEIR MEASURES

Essential Question: How can you create formulas to find the

distance between two points in all 1-D and 2-D situations?

Definitions

Postulates or Axioms – in geometry are rules that are accepted without proof.

Postulate 1 “Ruler Postulate”The points on a line can be matched one to

one with real #’s. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B.

AB is also called the length of .

Example 1 Find the length of AB.

A B2.3 5.4

Example 2 Find the length of CD.C D-5.1 -1.3

Postulate 2 Segment Addition PostulateIf B is between A and C, the AB + BC = AC.If AB + BC = AC, then B is between A and

C. A B C

Ex. 2 Find the distance from Denver to Boston (AC).

Denver Detroit BostonA B C

AB = 623 milesBC = 500 miles

Example 3 Find the distance from Detroit to Boston.

Denver Detroit BostonA B C

AB = 531 milesAC = 1021 miles

Example 4 Use the segment addition postulate to find MP. (Two column Proof Format)

M N O P

Step Reason

Example 5 Solve for all segment lengths:B is between A and CAB = 4x – 3BC = 3x + 8AC = 26