Question

which statements are true regarding the diagram? check all that apply.
□ cb is contained on line n.
□ ce is contained on line m.
□ ray bc is the same as ray cb.
□ ray ad is the same as ray ac.
□ ∠ead is created from ae and da.
□ ∠ecb is created from ce and cb.

Explanation:

Step1: Recall line - segment and ray concepts

A line - segment is part of a line. A ray has a starting point and extends infinitely in one direction.

Step2: Analyze statement 1

$\overline{CB}$ is a line - segment. From the diagram, $\overline{CB}$ lies on line $n$. So, “$\overline{CB}$ is contained on line $n$” is true.

Step3: Analyze statement 2

$\overrightarrow{CE}$ starts at $C$ and extends towards $E$. It lies on line $m$. So, “$\overrightarrow{CE}$ is contained on line $m$” is true.

Step4: Analyze statement 3

Ray $\overrightarrow{BC}$ starts at $B$ and goes towards $C$, while ray $\overrightarrow{CB}$ starts at $C$ and goes towards $B$. They are not the same. So, “Ray $BC$ is the same as ray $CB$” is false.

Step5: Analyze statement 4

Ray $\overrightarrow{AD}$ starts at $A$ and goes towards $D$, ray $\overrightarrow{AC}$ starts at $A$ and goes towards $C$. Since $D$ and $C$ are different points, “Ray $AD$ is the same as ray $AC$” is false.

Step6: Analyze statement 5

$\angle EAD$ is formed by rays $\overrightarrow{AE}$ and $\overrightarrow{AD}$, not $\overrightarrow{AE}$ and $\overrightarrow{DA}$. So, “$\angle EAD$ is created from $\overrightarrow{AE}$ and $\overrightarrow{DA}$” is false.

Step7: Analyze statement 6

$\angle ECB$ is formed by rays $\overrightarrow{CE}$ and $\overrightarrow{CB}$. So, “$\angle ECB$ is created from $\overrightarrow{CE}$ and $\overrightarrow{CB}$” is true.

Answer:

$\overline{CB}$ is contained on line $n$.
$\overrightarrow{CE}$ is contained on line $m$.
$\angle ECB$ is created from $\overrightarrow{CE}$ and $\overrightarrow{CB}$.