Question

Theorem 1-1 states that two lines intersect at exactly one point. The diagram suggests what would happen if you tried to show two “lines” drawn through two points. State the postulate that makes this situation impossible.

Short answer

The postulate that makes the situation impossible is “The postulate 6 which states that through any two points there is exactly one line.”

Step-by-step solution

Step 1. State Theorem 1-1

Theorem 1-1 states that two lines intersect only at one point.

Step 2. Observe the diagram.

The given diagram

Shows two lines drawn through two points.

Step 3. State postulate 6.

In order to state a postulate, which proves the given situation impossible is postulate 6. Postulate 6 states that “Through any two points there is exactly one line.

Therefore, postulate 6 proves the situation impossible.