MEASURING LENGTH Page 42

Length· Define length and congruent.· Identify and use the Segment Addition Postulate.

In defining the length of a segment, we will use anumber line, which is like a ruler. A number line isa line that has been set up to correspond with thereal numbers.

The coordinate of a point on a number line is a real number.In the illustration above, 5 is the coordinate of point A and 4is the coordinate of point B.

How would you find the distance between points A and B?

Length of AB (1.2.1) Let A and B be points on a number line, with coordinatesa and b. Then the measure of AB, which is called itslength, is |a - b| or |b - a|.

EXAMPLESFind the measures (lengths) of AB, AT, AND TB on thenumber line.

Congruent ( ≅ ) SegmentsCongruent figures are figures that are the same size andshape.

Which segments are congruent?

Segment Congruence Postulate (1.2.2) (BLUE)If 2 segments have the same length as measured by a fairruler, then the segments are ≅. Also, if 2 segments are ≅,then they have the same length as measured by a fair ruler.

Segment Addition Postulate (1.2.3) If point R is between points P and Q on a line, thenPR + RQ = PQ.

EXAMPLEThe towns of Squidward, Patrick, and Plankton are locatedalong a straight road. Patrick is between Squidward andPlankton. The distance from Squidward to Patrick is 13 milesmore than 5 times the distance from Patrick to Plankton. Thedistance Squidward to Plankton is 103 miles. Find the distance from Squidward to Patrick and from Patrick to Plankton.

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