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:

Step1: Analyze intersection of planes

In the figure, we can see planes $O$ and $M$ meet along a set of common points which form line $t$.

Step2: Identify postulate

The postulate that two non - parallel planes intersect in a line is used. This shows planes $O$ and $M$ intersect in line $t$.

Step3: Analyze line in plane

For line $p$ in plane $N$, we observe that all points of line $p$ are within the flat surface of plane $N$.

Step4: Identify postulate

The postulate that if two points of a line lie in a plane, then the entire line lies in the plane is used. If we assume two points on line $p$ are in plane $N$, then line $p$ lies in plane $N$.

Answer:

1. In the figure, planes $O$ and $M$ are shown to meet along line $t$, so they intersect in line $t$. The postulate is: If two non - parallel planes intersect, then their intersection is a line.
2. In the figure, all points of line $p$ are within plane $N$, so line $p$ lies in plane $N$. The postulate is: If two points of a line lie in a plane, then the entire line lies in the plane.