Question

analyzing rays and segments
which statements are true regarding the diagram?
check all that apply.
$overline{cb}$ is contained on line $n$.
$overrightarrow{ce}$ is contained on line $m$.
ray $bc$ is the same as ray $cb$.
ray $ad$ is the same as ray $ac$.
$\angle ead$ is created from $overrightarrow{ae}$ and $overrightarrow{da}$.
$\angle ecb$ is created from $overrightarrow{ce}$ and $overrightarrow{cb}$.

Explanation:

1. For $\overline{CB}$: Line \( n \) passes through \( A \) and has a direction, and \( \overline{CB} \) is not on line \( n \), so this is false.
2. For \( \overrightarrow{CE} \): Line \( m \) has the ray \( \overrightarrow{CE} \) along it, so \( \overrightarrow{CE} \) is on line \( m \), this is true.
3. Ray \( BC \) starts at \( B \) going to \( C \), ray \( CB \) starts at \( C \) going to \( B \) – different, so false.
4. Ray \( AD \) and ray \( AC \): Both start at \( A \) and go through \( C \) (and \( D \) is on the same line from \( A \) through \( C \)), so they are the same, true.
5. \( \angle EAD \): It should be from \( \overrightarrow{AE} \) and \( \overrightarrow{AD} \), not \( \overrightarrow{DA} \), so false.
6. \( \angle ECB \): Formed by \( \overrightarrow{CE} \) and \( \overrightarrow{CB} \), true.

Answer:

• \( \boldsymbol{\overrightarrow{CE}} \) is contained on line \( m \).
• Ray \( AD \) is the same as ray \( AC \).
• \( \boldsymbol{\angle ECB} \) is created from \( \boldsymbol{\overrightarrow{CE}} \) and \( \boldsymbol{\overrightarrow{CB}} \).