Practical Geometry - Construction of a Line Segment

A line segment is a portion of a line that has two fixed endpoints. It is the shortest distance between two points and has a definite length. Visually, it appears as a straight path with a dot at each end, labeled with capital letters like $A$ and $B$, and is written as $\overline{AB}$.

Measuring a line segment involves placing the zero ($0$) mark of a ruler at one endpoint and reading the value at the second endpoint. For accuracy, the eye should be placed vertically above the mark to avoid parallax error, which is a visual shift that occurs when an object is viewed from an angle.

A ruler (or scale) is a primary tool in practical geometry. One edge is usually divided into centimeters ($\text{cm}$) and the other into inches. Each centimeter is further divided into $10$ smaller parts called millimeters ($\text{mm}$), representing the relationship $1\text{ cm} = 10\text{ mm}$.

Constructing a line segment of a specific length using a compass is considered more accurate than using only a ruler. To do this, place the metal pointer of the compass on the ruler's $0$ mark and open the compass until the pencil point reaches the desired measure. This distance is then transferred to a line by drawing an arc.

To construct a copy of a given line segment $\overline{AB}$ without knowing its numerical length, use a compass to 'fix' the distance between the two endpoints $A$ and $B$. Then, without changing the compass width, place the pointer on a new point $P$ and draw an arc to mark point $Q$. The resulting $\overline{PQ}$ is a congruent copy of $\overline{AB}$.

Line segments can be compared or combined. If a point $C$ lies on the line segment $\overline{AB}$, then the length of the whole segment is the sum of its parts: $AB = AC + CB$. Visually, this means placing two segments end-to-end on a straight line to find their total length.