Question

the plane that contains points a, b, and g. plane c in exercises 5–8, use the diagram. 5. name one pair of opposite rays. 6. name two points that are collinear with point d. 7. name the point of intersection of line cd with plane a. 8. name a point that is not coplanar with plane a.

Explanation:

Question 5

Step1: Recall opposite rays definition

Opposite rays share the same endpoint and form a straight line (180° angle).

Step2: Identify from diagram

From the diagram, rays \( \overrightarrow{EG} \) and \( \overrightarrow{EF} \) share endpoint \( E \) and lie on a straight line, so they are opposite rays. (Other possible pairs: \( \overrightarrow{EC} \) and \( \overrightarrow{ED} \) as they share \( E \) and form a straight line too.)

Step1: Recall collinear points definition

Collinear points lie on the same line.

Step2: Identify line with D

Line \( CD \) contains point \( D \), so points \( C \) and \( E \) (or \( C \), \( E \), \( D \) – any two on line \( CD \)) are collinear with \( D \).

Step1: Recall line - plane intersection

The intersection of a line and a plane is a point (if the line is not parallel and not in the plane).

Step2: Identify intersection point

Line \( CD \) intersects plane \( A \) at point \( E \) (from the diagram, line \( CD \) passes through \( E \) which is in plane \( A \)).

Answer:

\( \overrightarrow{EG} \) and \( \overrightarrow{EF} \) (or \( \overrightarrow{EC} \) and \( \overrightarrow{ED} \))

Question 6