Question

analyzing rays and segments. 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 ray - segment definitions

A line segment is part of a line with two endpoints. A ray has one endpoint and extends infinitely in one direction. An angle is formed by two rays with a common endpoint.

Step2: Analyze each statement

Statement 1: $\overline{CB}$ is contained on line $n$.

From the diagram, point $C$ and $B$ are on line $n$, so the line - segment $\overline{CB}$ is on line $n$. This statement is true.

Statement 2: $\overrightarrow{CE}$ is contained on line $m$.

$\overrightarrow{CE}$ starts at $C$ and goes towards $E$. It is on line $n$, not line $m$. This statement is false.

Statement 3: Ray $\overrightarrow{BC}$ is the same as ray $\overrightarrow{CB}$.

Ray $\overrightarrow{BC}$ starts at $B$ and goes through $C$ infinitely, while ray $\overrightarrow{CB}$ starts at $C$ and goes through $B$ infinitely. They are different rays. This statement is false.

Statement 4: Ray $\overrightarrow{AD}$ is the same as ray $\overrightarrow{AC}$.

Ray $\overrightarrow{AD}$ starts at $A$ and goes through $D$ infinitely, and ray $\overrightarrow{AC}$ starts at $A$ and goes through $C$ infinitely. Since $D$ and $C$ are on the same line and in the same direction from $A$, ray $\overrightarrow{AD}$ and ray $\overrightarrow{AC}$ are the same ray. This statement is true.

Statement 5: $\angle EAD$ is created from $\overrightarrow{AE}$ and $\overrightarrow{DA}$

$\angle EAD$ should be created from $\overrightarrow{AE}$ and $\overrightarrow{AD}$. $\overrightarrow{DA}$ is in the opposite direction. This statement is false.

Statement 6: $\angle ECB$ is created from $\overrightarrow{CE}$ and $\overrightarrow{CB}$

$\angle ECB$ is formed by the two rays $\overrightarrow{CE}$ and $\overrightarrow{CB}$ with the common endpoint $C$. This statement is true.

Answer:

$\overline{CB}$ is contained on line $n$, Ray $\overrightarrow{AD}$ is the same as ray $\overrightarrow{AC}$, $\angle ECB$ is created from $\overrightarrow{CE}$ and $\overrightarrow{CB}$