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## 1.3 Segments and Their Measures

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**1.3Segments and Their Measures**Objectives: Use the Segment Addition Postulate. Use the Distance Formula to find the distance between two points.**Basic Vocabulary**Postulate • a rule that is accepted as true without proof Theorem • a rule that must be proven true.**names of thepoints**coordinates of thepoints The distance between points A and B or the length of AB Postulates • Ruler Postulate A B x1 x2 AB = | x2 – x1|**Postulates**• Segment Addition Postulate If B is between A and C then AB + BC = AC A B C This indicates that the points are collinear.**AB**BC AC Postulates • Segment Addition Postulate If B is between A and C then AB + BC = AC A B C The pieces of a segment add up to the whole segment.**AB**BC AC Postulates • Segment Addition Postulate If A, B , and C are collinear and AB + BC = AC then B is between A and C A B C The postulate also works in reverse**Example 1:**E D F**9**35 Example 2: x E x D C B A**2**20 Practice 1: x 2x D C B A**425 yds**267 yds Example 3: Find the distance between Sue’s house and Jane’s house. 425 + 267 692 yds**15 feet**Example 4: A truck with a trailer has a total length of 27 feet. If the trailer has a length of 15 feet, how long is the truck? 12 feet 27 – 15 27 feet**y**x Theorem The Distance Formula If A(x1, y1) and B(x2, y2) are points on a coordinate plane then the distance between A and B is A B C**the symbol for congruent**this represents a number equal to a number this represents a figure the same size and shape as another figure Definition Congruent Segments segments that have the same length B Y A X**y**x Example 5: Find the lengths of the segments. Are any of the segments congruent?**y**x Example 5: Find the lengths of the segments. Are any of the segments congruent?**y**x Example 5: none of the segments are congruent Find the lengths of the segments. Are any of the segments congruent?**Practice 3:**Find the distance between the points. A (3, 1) B (0, 4)**Summary**What is a postulate? Describe how to use the Segment Addition Postulate. Describe how to use the Distance Formula