Perry draws two planes, K and L, as shown.




Which statement is true?

Plane K and plane L contain four lines because a theorem states that a line extends on both sides of a plane.

Plane K and plane L intersect along a line because a postulate states that if two planes intersect, then their intersection is a line.

Plane K and plane L intersect along two lines because a theorem states that there are only two planes that can pass through a line.

Plane K and plane L make a straight angle with each other because a postulate states that the measure of a straight angle is two right angles.

The correct statement is: Plane K and plane L intersect along a line because a postulate states that if two planes intersect, then their intersection is a line.

To determine which statement is true, we need to analyze the information given in the question.

The question mentions two planes, K and L. It is important to understand some basic concepts related to planes:

1. A plane is a flat, two-dimensional surface that extends infinitely in all directions.
2. A line is a straight path that extends infinitely in both directions.
3. The intersection of two planes can result in a line, a point, or no intersection at all.

Let's evaluate each statement:

1. "Plane K and plane L contain four lines because a theorem states that a line extends on both sides of a plane."

This statement is not true. While it is correct that a line extends infinitely on both sides, the question does not provide any information about lines within the planes K and L.

2. "Plane K and plane L intersect along a line because a postulate states that if two planes intersect, then their intersection is a line."

This statement is plausible. According to the given postulate, when two planes intersect, their intersection is a line. However, it does not explicitly state that the planes K and L intersect.

3. "Plane K and plane L intersect along two lines because a theorem states that there are only two planes that can pass through a line."

This statement is not accurate. The theorem mentioned here refers to a different concept - it states that there are only two planes that can be drawn through a given line, not that the intersection of two planes results in two lines.

4. "Plane K and plane L make a straight angle with each other because a postulate states that the measure of a straight angle is two right angles."

This statement is not relevant to planes intersecting. A straight angle is formed by a line and consists of two opposite rays. It does not address the intersection of planes.

Based on the information provided, the statement that seems most relevant and plausible is statement 2: "Plane K and plane L intersect along a line because a postulate states that if two planes intersect, then their intersection is a line." However, without further information about the actual drawing of the planes K and L, we cannot determine with certainty which statement is true.