Question

which statements are true regarding the diagram? check all that apply. cb is contained on line x. 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 ad. ∠ecb is created from ce and cb.

Explanation:

Step1: Recall line - segment and ray properties

A line contains all the points on it. A ray has a starting - point and extends infinitely in one direction. An angle is formed by two rays with a common endpoint.

Step2: Analyze statement 1

$\overline{CB}$ is a line - segment. Point C and B lie on line $x$, so $\overline{CB}$ is contained on line $x$. This statement is true.

Step3: Analyze statement 2

There is no $\overrightarrow{CE}$ clearly defined in the problem description in a way that it is contained on line $m$. This statement is false.

Step4: Analyze statement 3

Ray $BC$ starts at point B and extends through C, while ray $CB$ starts at point C and extends through B. They are not the same. This statement is false.

Step5: Analyze statement 4

Ray $AD$ starts at point A and extends through D, and ray $AC$ starts at point A and extends through C. Since D and C are different points, ray $AD$ is not the same as ray $AC$. This statement is false.

Step6: Analyze statement 5

$\angle EAD$ is formed by rays $\overrightarrow{AE}$ and $\overrightarrow{AD}$. This statement is true.

Step7: Analyze statement 6

$\angle ECB$ is formed by rays $\overrightarrow{CE}$ and $\overrightarrow{CB}$. This statement is true.

Answer:

$\overline{CB}$ is contained on line $x$; $\angle EAD$ is created from $\overrightarrow{AE}$ and $\overrightarrow{AD}$; $\angle ECB$ is created from $\overrightarrow{CE}$ and $\overrightarrow{CB}$