1.2 Use Segments and Congruence

Objectives:

Understand segments have measures.

Apply properties of segments

Postulates

In geometry, a postulate or axiom is a statement that describes a fundamental relationship between the basic terms of geometry.

Postulates are always accepted as true.

Ruler Postulate

Postulate 1 (Ruler Postulate)The points on any line or line segment can be paired with real numbers so that, given any two points A and B on a line, A corresponds to zero, and B corresponds to a positive real number.

Basically, all segments have a positive measure.

Distance Formula on a Number Line

If a segment is on a number line, we simply find its length by using the Distance Formula which states the distance between two points is the absolute value of the difference of the values of the two points.

| A – B | = | B – A | = Distance

Measures

Measures are real numbers, thus all arithmetic properties can be applied.

Postulate 2 (Segment Addition Postulate)If we have a line segment divided into parts, then by applying a relationship called betweenness of points we know the measure of each segment added together equals the measurement of the entire segment.

AB + BC = ACA B C

Congruent Segments

When segments have the same measure, they are said to be congruent ( ).

is read “is congruent to.” Slashes on the line segments also indicate the segments are congruent.

AB CDA B

C

D

More About Congruency Note, when we are discussing segments we draw

a line over the endpoints, AB, but when we are discussing the measure of segments we simply write the letters. Likewise, we must also be sure that when we are comparing segments we use the congruent sign, but when we are comparing their measures we use an equal sign.

Never intermix the two symbols.

AB CD segmentsAB = CD measures

Assignment:

Geometry Pg. 12 - 14, #6 - 31