Geometry 1 3 Segments and Their Measures Using

Geometry 1. 3 Segments and Their Measures

Using Segment Postulates In geometry, rules that are accepted without proof are called postulates or axioms. Rules that are proved are called theorems.

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 x 1 x 2 Coordinates of points A B x 1 x 2 AB = x 1 - x 2

How long is this line?

When three points lie on a line, you can say that one of them is between the other two. This concept applies to collinear points only.

POSTULATE 2: SEGMENT ADDITION POSTULATE If B is between A and C, then AB + BC = AC. A B C If AB + BC = AC, the B is between A and C

The Segment Addition Postulate can be generalized to three or more segments, as long as the segments lie on the same line Ex: If A, B, C, and D lie on the same line then AD = AB + BC + CD

Using Segment Addition Postulate If AB = 12 and BC = 8, how long is AC?

Using Segment Addition Postulate Find the measure of XY

PYTHAGOREAN THEOREM

Distance Formula If A(x 1, y 1) and B(x 2, y 2) are points in a coordinate plane, then the distance between A and B is

Find the lengths of AB B C AC AD A D

AB = square root of 13 AC = square root of 17 AD = square root of 13

Segments that have the same length are called congruent segments