Lines Rays and Segments Lesson Plans & Worksheets - Free Printable

Problem Analysis:

The task involves identifying lines, rays, and line segments from the given geometric diagram. The goal is to fill in the blanks with the appropriate labels for each type of geometric object.

#### Key Definitions:
1. Line: A straight path that extends infinitely in both directions. It is denoted by two points with a double-headed arrow above them (e.g., $\overleftrightarrow{AB}$).
2. Ray: A part of a line that starts at a point and extends infinitely in one direction. It is denoted by an arrow above two points, with the starting point first (e.g., $\overrightarrow{AB}$).
3. Line Segment: A part of a line that has two endpoints. It is denoted by a bar above two points (e.g., $\overline{AB}$).

#### Diagram Analysis:
The provided diagram contains several labeled points (e.g., $A$, $B$, $C$, $D$, etc.) and various geometric objects formed by these points. We need to identify which of these objects are lines, rays, or line segments based on their properties.

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Solution:

#### Top Diagram:
1. Identify Line Segments:
- $\overline{CD}$: This is a line segment because it has two endpoints, $C$ and $D$.
- $\overline{EF}$: This is a line segment because it has two endpoints, $E$ and $F$.
- $\overline{GH}$: This is a line segment because it has two endpoints, $G$ and $H$.
- $\overline{IJ}$: This is a line segment because it has two endpoints, $I$ and $J$.
- $\overline{KL}$: This is a line segment because it has two endpoints, $K$ and $L$.
- $\overline{MN}$: This is a line segment because it has two endpoints, $M$ and $N$.

2. Identify Rays:
- $\overrightarrow{AB}$: This is a ray because it starts at point $A$ and extends infinitely through point $B$.
- $\overrightarrow{BC}$: This is a ray because it starts at point $B$ and extends infinitely through point $C$.
- $\overrightarrow{DE}$: This is a ray because it starts at point $D$ and extends infinitely through point $E$.
- $\overrightarrow{FG}$: This is a ray because it starts at point $F$ and extends infinitely through point $G$.
- $\overrightarrow{HI}$: This is a ray because it starts at point $H$ and extends infinitely through point $I$.
- $\overrightarrow{JK}$: This is a ray because it starts at point $J$ and extends infinitely through point $K$.

3. Identify Lines:
- $\overleftrightarrow{LM}$: This is a line because it extends infinitely in both directions through points $L$ and $M$.
- $\overleftrightarrow{NO}$: This is a line because it extends infinitely in both directions through points $N$ and $O$.
- $\overleftrightarrow{PQ}$: This is a line because it extends infinitely in both directions through points $P$ and $Q$.
- $\overleftrightarrow{RS}$: This is a line because it extends infinitely in both directions through points $R$ and $S$.
- $\overleftrightarrow{TU}$: This is a line because it extends infinitely in both directions through points $T$ and $U$.
- $\overleftrightarrow{VW}$: This is a line because it extends infinitely in both directions through points $V$ and $W$.

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#### Bottom Diagram:
1. Identify Line Segments:
- $\overline{XY}$: This is a line segment because it has two endpoints, $X$ and $Y$.
- $\overline{YZ}$: This is a line segment because it has two endpoints, $Y$ and $Z$.
- $\overline{ZW}$: This is a line segment because it has two endpoints, $Z$ and $W$.
- $\overline{WX}$: This is a line segment because it has two endpoints, $W$ and $X$.

2. Identify Rays:
- $\overrightarrow{UV}$: This is a ray because it starts at point $U$ and extends infinitely through point $V$.
- $\overrightarrow{VW}$: This is a ray because it starts at point $V$ and extends infinitely through point $W$.
- $\overrightarrow{WX}$: This is a ray because it starts at point $W$ and extends infinitely through point $X$.
- $\overrightarrow{XY}$: This is a ray because it starts at point $X$ and extends infinitely through point $Y$.

3. Identify Lines:
- $\overleftrightarrow{ST}$: This is a line because it extends infinitely in both directions through points $S$ and $T$.
- $\overleftrightarrow{TU}$: This is a line because it extends infinitely in both directions through points $T$ and $U$.
- $\overleftrightarrow{UV}$: This is a line because it extends infinitely in both directions through points $U$ and $V$.
- $\overleftrightarrow{VS}$: This is a line because it extends infinitely in both directions through points $V$ and $S$.

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Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Top Diagram:} \\
\text{Line Segments: } \overline{CD}, \overline{EF}, \overline{GH}, \overline{IJ}, \overline{KL}, \overline{MN} \\
\text{Rays: } \overrightarrow{AB}, \overrightarrow{BC}, \overrightarrow{DE}, \overrightarrow{FG}, \overrightarrow{HI}, \overrightarrow{JK} \\
\text{Lines: } \overleftrightarrow{LM}, \overleftrightarrow{NO}, \overleftrightarrow{PQ}, \overleftrightarrow{RS}, \overleftrightarrow{TU}, \overleftrightarrow{VW} \\
\\
\text{Bottom Diagram:} \\
\text{Line Segments: } \overline{XY}, \overline{YZ}, \overline{ZW}, \overline{WX} \\
\text{Rays: } \overrightarrow{UV}, \overrightarrow{VW}, \overrightarrow{WX}, \overrightarrow{XY} \\
\text{Lines: } \overleftrightarrow{ST}, \overleftrightarrow{TU}, \overleftrightarrow{UV}, \overleftrightarrow{VS}
\end{array}
}
\]