Measuring Segments
Overview
A segment can be measured, and its measure is the distance between its endpoints. On a number line, that distance is the absolute value of the difference of the two coordinates. On the coordinate plane, distance comes from the Distance Formula, which is the Pythagorean Theorem in disguise. Segments with equal measures are congruent, and the bar notation matters: the name of a segment and the number that measures it are different things.
Vocabulary
- Measure of a Segment
- The distance between the segment's endpoints. The measure of segment AB is written AB (with no bar above it): the name with the bar names the segment itself, while the name without the bar is a number.
- Congruent Segments
- Segments that have equal measures. Two segments are congruent if and only if their measures are equal.
- Distance on a Number Line
- The distance between two points on a number line is the absolute value of the difference of their coordinates, so distance is never negative.
- Distance Formula
- The distance between A(x₁, y₁) and B(x₂, y₂) in the coordinate plane is d = √((x₂ − x₁)² + (y₂ − y₁)²).
- Endpoint
- A point at the end of a segment or at the starting point of a ray. A segment has two endpoints.
Main Ideas
- Congruence of segments is decided by measures: equal numbers mean congruent segments.
- Distance is always nonnegative — take the absolute value of the difference on a number line.
- The Distance Formula averages nothing; it combines the horizontal change and the vertical change as the legs of a right triangle.
- Subtract coordinates in the same order in both parts of the formula, and square before adding — never add the differences and then take a square root of the sum unsquared.
Lesson Notes
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Lesson Video
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Interactive Activity
Measure segments on a number line and with coordinates, and work with the distance formula.
Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.