Question

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 part 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 rays that do not share an endpoint (e.g., two rays pointing in different directions with no common starting - point).

Step2: Draw and name adjacent angles for part B

Draw two adjacent angles $\angle ABC$ and $\angle CBD$. The possible ways to name $\angle ABC$ are $\angle ABC$, $\angle CBA$, $\angle B$ (when the vertex $B$ is unambiguous). For $\angle CBD$, it can be named $\angle CBD$, $\angle DBC$, $\angle B$ (when it is clear which of the two adjacent angles at $B$ is meant). The combined angle $\angle ABD$ can be named $\angle ABD$, $\angle DBA$.

Step3: Draw non - adjacent angles for part C

Draw two angles $\angle ABC$ and $\angle DBE$ that share the vertex $B$ but are not adjacent. For example, have the rays of the two angles cross each other in such a way that they do not share a common side between them.

Answer:

A. (Draw two rays with a common endpoint for the first part and two non - intersecting rays for the second part).
B. (Draw adjacent angles $\angle ABC$ and $\angle CBD$. Names for $\angle ABC$: $\angle ABC$, $\angle CBA$, $\angle B$; for $\angle CBD$: $\angle CBD$, $\angle DBC$, $\angle B$; for $\angle ABD$: $\angle ABD$, $\angle DBA$).
C. (Draw two angles $\angle ABC$ and $\angle DBE$ sharing vertex $B$ but not adjacent).