Questions: Main Street intersects Avenue A and Avenue B. Avenue A is parallel to Avenue B. Avenue A is also perpendicular to Main Street. How are Avenue B and Main Street related? Explain. Choose the correct answer below. A. Avenue B and Main St Next will be perpendicular by the Perpendicular Transversal Theorem since Avenue A is parallel to Avenue B. B. Avenue B and Main Street will be perpendicular by the Perpendicular Postulate since Avenue A is parallel to Avenue B. C. Avenue B and Main Street will be parallel by the Parallel Postulate since Avenue A is parallel to Avenue B. D. Avenue B and Main Street will be parallel by the Two Lines Parallel to a Third Line Theorem since Avenue A parallel to Avenue B.

Solution Steps

To determine the relationship between Avenue B and Main Street, we need to use the properties of parallel and perpendicular lines. Since Avenue A is parallel to Avenue B and Avenue A is perpendicular to Main Street, we can infer the relationship between Avenue B and Main Street using these properties.

1. If two lines are parallel to each other and one of them is perpendicular to a third line, then the other line must also be perpendicular to that third line.

We are given the following information:

• Avenue \( A \) is parallel to Avenue \( B \).
• Avenue \( A \) is perpendicular to Main Street.

Using the properties of parallel and perpendicular lines:

• If two lines are parallel to each other and one of them is perpendicular to a third line, then the other line must also be perpendicular to that third line.

Since Avenue \( A \parallel \) Avenue \( B \) and Avenue \( A \perp \) Main Street, it follows that Avenue \( B \perp \) Main Street.

Final Answer