P. 6 (17-22) TOGETHER

1.2: USE SEGMENTS AND CONGRUENCE

“A rule that is accepted without proof ”

DEFINE: POSTULATE

Also called an axiom

The points on a line can be matched to one with the real numbers. The real number that corresponds to a point is the coordinate of the point.

POSTULATE 1: RULER POSTULATE

The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates.

A B

x1 x2

EXAMPLE 1

POSTULATE 2: SEGMENT ADDITION POSTULATE

If B is between A and C, then AB + BC = AC

A B C

AB BC

AC

EXAMPLE 2

EXAMPLE 3

EXAMPLE 4

CONGRUENT SEGMENTS

Line segments that have the same length are called congruent segments

A

D C

B Lengths are Equal

Segments are congruent

AB = CD AB = CD

EXAMPLE 5

EXAMPLE 6

EXAMPLE 7

HOMEWORK P. 12 (6-27)