Question

defined terms
term figure names
a ray is a part of a line that starts at an endpoint and extends forever in one direction.
an angle is formed by two line - segments or rays that share the same endpoint.
a vertex of an angle is the common endpoint of the two rays that form the angle.
adjacent angles are two angles in the same plane with a common vertex and a common side, but no common interior points.
task 1:
a. draw two rays that form an angle. draw two rays that do not form an angle.
b. draw and label adjacent angles abc and cbd. write all possible ways to name all three angles using the point names.
c. draw and label angles abc and dbe so that they share the vertex b but are not adjacent angles.

Explanation:

Step1: Draw rays for an angle

Draw two rays $\overrightarrow{OA}$ and $\overrightarrow{OB}$ with a common - endpoint $O$. They form $\angle AOB$. To draw two rays that do not form an angle, draw two non - intersecting rays, for example, $\overrightarrow{PQ}$ and $\overrightarrow{RS}$ where the rays have no common endpoint.

Step2: Draw and name adjacent angles

Draw $\overrightarrow{BA}$, $\overrightarrow{BC}$, and $\overrightarrow{BD}$ such that $\angle ABC$ and $\angle CBD$ are adjacent angles.

• $\angle ABC$ can also be named $\angle CBA$ and $\angle B$.
• $\angle CBD$ can also be named $\angle DBC$ and $\angle B$ (when the context is clear that it refers to $\angle CBD$).
• $\angle ABD$ can be named $\angle DBA$.

Step3: Draw non - adjacent angles sharing a vertex

Draw $\overrightarrow{BA}$, $\overrightarrow{BC}$, $\overrightarrow{BE}$, and $\overrightarrow{BD}$ such that $\angle ABC$ and $\angle DBE$ share the vertex $B$ but have no common side between them.

Answer:

A. For two rays that form an angle: Draw two rays with a common endpoint. For two rays that do not form an angle: Draw two non - intersecting rays with no common endpoint.
B. For adjacent angles $\angle ABC$ and $\angle CBD$: $\angle ABC$ can be named $\angle CBA,\angle B$; $\angle CBD$ can be named $\angle DBC,\angle B$; $\angle ABD$ can be named $\angle DBA$.
C. Draw two angles with the same vertex but no common side between them.