Understanding Elementary Shapes - Measuring Line Segments

A line segment is a fixed portion of a line that has two distinct endpoints. It is typically represented as $\overline{AB}$, showing a straight path connecting point $A$ and point $B$.

Comparison by observation involves looking at two line segments to decide which is longer. While simple, this method is often inaccurate, especially when the difference in length is very small, such as two segments appearing nearly identical to the naked eye.

Comparison by tracing involves using tracing paper to copy one segment and placing it over another. The accuracy of this method depends entirely on how precisely the segment is traced and then compared visually.

Measurement using a ruler is the most common method. A standard ruler is divided into $15$ centimeters ($cm$), where each centimeter is further divided into $10$ smaller parts called millimeters ($mm$). A segment's length is determined by placing the $0$ mark at one end and reading the value at the other end.

The divider is a tool with two metal points used for more accurate measurements. By placing the points of the divider on the endpoints of a line segment and then lifting it to place it on a ruler, we avoid errors caused by the thickness of the ruler.

Parallax error occurs when the eye is not positioned vertically above the mark being read on the ruler. To avoid this, the eye must be placed directly over the point of measurement to ensure the reading is exact.

A point $C$ is said to lie between points $A$ and $B$ only if $A, B,$ and $C$ are collinear (on the same line) and the sum of the lengths of the smaller segments equals the total length, expressed as $AC + CB = AB$.

The midpoint of a line segment is a point that divides the segment into two equal halves. Visually, if $M$ is the midpoint of $\overline{AB}$, then the distance from $A$ to $M$ is the same as the distance from $M$ to $B$.