1.1.2 Measuring and Constructing Segments (continued)
In this example a number line is given with the points X , Z , Y , and W , named on the number line. The coordinate of each point is the number that corresponds with that point. So, the coordinate of W is 3. To find XW , first identify coordinates of its endpoints: − 7 and 3. Then subtract these coordinates (in either order) and take the absolute value of the difference. Here, the length of the segment was found by subtracting − 7 from 3. Note that subtracting in the reverse order results in the same length. | − 7 − 3| = | − 10| = 10 Notice that the segment from X to W is represented here as XW and as XW . The notation XW refers to the length of the segment, so XW is equal to a number (in this case XW = 10). The notation XW refers to the segment itself. When two segments have the same length, they are congruent. The symbol for congruent is similar to the symbol = , but the congruent symbol has a squiggle over the = . The difference between congruent and equal is that segments themselves can be congruent, while the lengths of segments can be equal. Small dashes, called tick marks, are drawn in figures to indicate that segments are congruent.
Example 2 Copying a Segment
A sketch of a figure is an approximate version of a figure. A construction is a way of creating a figure that is more precise than a sketch. One way to make a geometric construction is to use a compass and straightedge.
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