1.1.2 Measuring and Constructing Segments (continued) Example 3 Using the Segment Addition Postulate

In order for you to say that a point B is between two points A and C , all three of the points must lie on the same line, and AB + BC = AC .

In this example, the fact that B is between A and C is given. So, by the Segment Addition Postulate, it must be true that AB + BC = AC . Use the given information to sketch a segment. Since B is between A and C , the segment’s endpoints must be A and C . Now label the segment with the given lengths AC = 25 and BC = 7.2. From the sketched segment it is easy to see that AB + BC = AC , or AB + 7.2 = 25. Solve this equation by subtracting 7.2 from both sides to find AB. The length of AB is 25 − 7.2, or 17.8. The figure is given in this example. Begin by identifying the given information from the figure. The bar to the left of the segment extending from P to Q indicates that the corresponding expression, 9 x , represents PQ (read “ PQ ” as “the length of line segment PQ ”), or PQ = 9 x . To the right of the segment is 19 and 6 x − 1. The placement of 19 between P and R indicates that PR = 19, and the placement of 6 x − 1 between R and Q indicates that RQ = 6 x − 1. Furthermore, since P and Q are the endpoints of a segment containing R , R must be between P and Q . Therefore, by the Segment Addition Postulate, PR + RQ = PQ . Substitute the given lengths into this equation and solve for x . Note that x is not equal to PQ , but that PQ = 9 x . So, once the value of x is found, substitute that value into the expression 9 x to find PQ .

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