Question

identify all rays and lines in the picture below.
rays: \\( \overrightarrow { b d } \\), \\( \overrightarrow { c a } \\), \\( \overrightarrow { a c } \\), \\( \overrightarrow { a b } \\)
lines: \\( \overleftrightarrow { a c } \\)
rays: \\( \overrightarrow { b d } \\), \\( \overrightarrow { a b } \\)
lines: \\( \overleftrightarrow { a c } \\), \\( \overleftrightarrow { b d } \\), \\( \overleftrightarrow { a b } \\)
rays: \\( \overrightarrow { b d } \\), \\( \overrightarrow { a b } \\)
lines: \\( \overleftrightarrow { a c } \\)
rays: \\( \overrightarrow { b d } \\), \\( \overrightarrow { a c } \\), \\( \overrightarrow { a b } \\)

Explanation:

Step1: Recall definitions

A ray has one endpoint and extends infinitely in one direction. A line extends infinitely in both directions.

Step2: Analyze $\overrightarrow{BD}$

It has endpoint $B$ and extends infinitely through $D$, so it is a ray.

Step3: Analyze $\overrightarrow{AB}$

It has endpoint $A$ and extends infinitely through $B$, so it is a ray.

Step4: Analyze $\overleftrightarrow{AC}$

It extends infinitely in both directions (through $A$ and $C$), so it is a line.

Step5: Check other options

$\overrightarrow{CA}$ and $\overrightarrow{AC}$ are lines (not rays as they extend infinitely in both directions). $\overleftrightarrow{BD}$ and $\overleftrightarrow{AB}$ are not lines in the given figure (as per the diagram's structure).

Answer:

Rays: $\overrightarrow{BD}$, $\overrightarrow{AB}$
Lines: $\overleftrightarrow{AC}$