Let's break down and answer the questions from the worksheet based on the provided figures.

Part 1: Using the figure to the right

a. What are two other ways to name $\overrightarrow{EF}$?

• $\overrightarrow{FE}$ is not valid because rays are directed.
• Another valid name for $\overrightarrow{EF}$ could be extended using points on the same ray, like $\overrightarrow{EB}$, if point B is on that ray.

b. What are two other ways to name plane $C$?

• Planes can be named by any three non-collinear points on the plane.
• Two other ways to name the plane could be plane GFE or plane GEB using three points that lie on the plane.

c. Name three collinear points.

• Collinear points are points that lie on the same straight line. From the diagram, three collinear points could be A, B, and C.

d. Name four coplanar points.

• Coplanar points lie on the same plane. In the diagram, points E, F, G, B are coplanar.

Part 2: Using the figure to the right

a. Name 6 segments in the figure.

• Segments are straight lines connecting two points. The six segments could be:
  • $AB$
  • $BC$
  • $CD$
  • $EF$
  • $EB$
  • $FB$

b. Name 6 different rays.

• Different rays originating from different points:
  • $\overrightarrow{BA}$
  • $\overrightarrow{BC}$
  • $\overrightarrow{CB}$
  • $\overrightarrow{EF}$
  • $\overrightarrow{BE}$
  • $\overrightarrow{BF}$

c. Name a pair of opposite rays with endpoint $B$.

• A pair of opposite rays with endpoint $B$ would be $\overrightarrow{BA}$ and $\overrightarrow{BC}$, as they extend in opposite directions from the same point.

Part 3: Using the figure to the right

a. Name the intersection of planes $QRS$ and $RSW$.

• The intersection of two planes is a line. The planes $QRS$ and $RSW$ intersect along line RS.

b. Are points $V, R, S$ collinear?

• No, the points V, R, S are not collinear because they do not lie on the same straight line in the 3D space shown.

c. Are points $V, R, S$ coplanar?

• Yes, points V, R, S are coplanar because they all lie on plane RSW.

Would you like further details or explanations on any of these? Here are five additional questions to consider:

1. How can you distinguish between collinear and coplanar points?
2. How would the intersection of two planes change if they were parallel?
3. Can three rays with a common endpoint form a plane? Why or why not?
4. What is the difference between a segment and a ray in terms of their definitions?
5. How can you use opposite rays to define a straight line?

Tip: When naming planes, remember that any three non-collinear points determine a unique plane.