Question

music explain how the figure illustrates that the statement is true. then state the postulate that can be used to show the statement is true. line p lies in plane n. points a and d both lie on select choice and in plane n. postulate: if two points lie select choice, then the entire select choice containing those points lies select choice.

Explanation:

Step1: Identify the line for points A and D

From the figure, points A and D lie on line \( p \) (visually, the line with arrow \( p \) passes through both A and D).

Step2: Recall the postulate

The postulate is: If two points lie in a plane, then the entire line containing those points lies in the plane. So, since A and D are in plane N (as line \( p \) is in plane N and they are on line \( p \)), by the postulate, line \( p \) (the line containing A and D) lies in plane N.

Answer:

• Points A and D both lie on \(\boldsymbol{\text{line } p}\) and in plane \( N \).
• Postulate: If two points lie \(\boldsymbol{\text{in a plane}}\), then the entire \(\boldsymbol{\text{line}}\) containing those points lies in the plane.
• So, line \( p \) lies in plane \( N \) because A and D (on line \( p \)) are in plane \( N \), satisfying the postulate.