Question

example 1 music explain how the figure illustrates that each statement is true. then state the postulate that can be used to show that each statement is true. 1. planes o and m intersect in line t. 2. line p lies in plane n.

Explanation:

1. Planes \( O \) and \( M \) Intersect in Line \( t \)

Step 1: Identify Intersection

From the figure, planes \( O \) (blue, lower) and \( M \) (blue, upper) share a common line \( t \) (the vertical red line).

Step 2: Apply Postulate

Postulate: If two planes intersect, their intersection is a line. Here, planes \( O \) and \( M \) intersect, so their intersection is line \( t \).

2. Line \( p \) Lies in Plane \( N \)

Step 1: Identify Line and Plane

Line \( p \) (vertical red at the top) is entirely within plane \( N \) (the blue region at the top).

Step 2: Apply Postulate

Postulate: If two points of a line lie in a plane, the entire line lies in the plane. Line \( p \) has points (e.g., \( D \)) in plane \( N \), so line \( p \) lies in plane \( N \).

Answer:

s:

1. Planes \( O \) and \( M \) intersect in line \( t \) (by the postulate: If two planes intersect, their intersection is a line).
2. Line \( p \) lies in plane \( N \) (by the postulate: If two points of a line lie in a plane, the entire line lies in the plane).