1.1.2 Measuring and Constructing Segments
Key Objectives • Use length and midpoint of a segment. • Construct midpoints and congruent segments. Key Terms • A coordinate is a number used to identify the location of a point. On a number line, a point corresponds to one number and this number is called a coordinate. • The distance between any two points is the absolute value of the difference of the coordinates. • The distance between two points A and B is also called the length of AB , or AB . • Congruent segments are segments that have the same length. • A construction is a way of creating a figure that is more precise than a sketch. • 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 . • The midpoint M of a segment AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of segment AB , then AM = MB . • To bisect is to divide into two congruent parts. • A segment bisector is any ray, segment, or line that intersects a segment at its midpoint. Formulas • Ruler Postulate The points on a line can be put into a one-to-one correspondence with the real numbers. Theorems, Postulates, Corollaries, and Properties • Segment Addition Postulate If B is between A and C , then AB + BC = AC . Example 1 Finding the Length of a Segment When a segment is drawn on a number line, each of the segment’s endpoints corresponds with exactly one real number on a number line, called a coordinate. The relationship between points and real numbers is described in the Ruler Postulate. The points on a line can be put into a one-to-one correspondence with the real numbers. In other words, when a segment is on a number line, there is exactly one number on that number line that corresponds with each endpoint. A segment is a part of a line that has a defined length. The length of a segment on a number line is the distance between its two endpoints, and the distance between any two points on a number line is the absolute value of the difference of the coordinates. So, to find the length of a segment on a number line, find the difference between the coordinates (the numbers at the endpoints), and then take the absolute value of that difference.
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