1.3 Segments & Their Measures

Objectives/Assignment Use Segment Postulates Use the Distance Formula to measure distances Assignment: 2-42 even, 60-70 even, practice quiz page 25

Goal 1: Using Segment Postulates In Geometry rules that are accepted without proof are called postulates or axioms. Rules that are proved are called theorems. In this lesson, you will study two postulates about the lengths of segments.

Postulate 1: Ruler Postulate The points on a line can be matched one to one with the real numbers. 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 AB. Names of points A B AB x1 x2 Coordinates of points AB = X2 – X1

Example: Find the distance between two points Point A is at 3 and B is at 5.5 So, AB = 5.5 - 3 = 2.5

Is Alex between Ty and Josh? Yes! Ty Alex Josh No, but why not? How about now? In order for a point to be between 2 others, all 3 points MUST BE collinear!!

Postulate 2: Segment Addition Postulate If B is between A & C, then AB + BC = AC. If AB + BC = AC, then B is between A & C. AC A B C AB BC

Example: if DE=2, EF=5, and DE=FG, find FG, DF, DG, & EG.

Goal 2: Using the Distance Formula If A (x1, y1) and B (x2, y2) are points in a coordinate plane, then the distance between A and B is AB = (x1,y1) & (x2,y2) are the 2 points. Let’s do an example on the board.

Distance Formula (cont.) The distance formula is based on the Pythagorean Theorem, which you will see again when you work with right triangles in Chapter 9. Pythagorean Theorem: a2+b2=c2 a & b are the lengths of the legs of a right triangle and c is the length of the hypotenuse.

Congruent ( ) Segments Segments that have the same length are congruent segments. If AB & XY have the same length, Then AB=XY, but AB XY Symbol for congruent