2 What you’ll learn How to define postulate How to identify and model line segmentsHow to apply the Segment Addition PostulateHow to compute with measuresHow to identify congruent segments
3 Vocabulary Terms: Postulate Line segment Betweeness of points Between Segment Addition PostulateUnit ConversionCongruent Segments
4 Postulates Geometry is based on accepted rules and proven theories. Postulate is the term used for rules that are assumed to be true (postulates do not have to be proven).
5 Line Segment—a section of a line from one endpoint to another endpoint Draw it with 2 dots (one at each end) and a straight line between themPQName it by the endpts (with above)Fact: Segments are measureable. They have a beginning and end. The measure of a segment is written by naming the endpts with capital printed letters (PQ means the measure of PQ)Words/Symbols:PQ
6 Segments are measured with a ruler, yardstick or tape measure Segments have measureSegments are measured with a ruler, yardstick or tape measureUnits of measure includeInchesFeetYardsCentimetersMeters
7 Unit Conversion Standard Students will be able to convert units of measurement within and between systemsWithin the same systemLike inches to feetBetween systemsLike inches to centimeters
8 BetweenessThere are infinitely many points between the endpoints of a line segmentGOFor ExampleGiven DGDWould it be fair to say O is between D and G?What relationships do you see between the points?Do the points have to be collinear?Is there some connection between the measures DO, OG and DG?
9 Betweeness and the Segment Addition Postulate O is between D and G if and only ifD, O , and G are collinearDO + OG = DG
10 Congruent Segments Congruent figures have the same size and shape Since all segments have the same shape we only need to verify that two segments have the same measure to be congruentDefinition of Congruent Segments:Two segments are congruent if and only if they have the same measure.Using symbols: AB CD iff AB = CDABCD
11 Have you learned. . . How to define postulate? How to identify and model line segments?How to apply the Segment Addition Postulate?How to compute with measures?How to identify congruent segments?Your assignment is Worksheet 1.2