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.

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.

Transcript text: 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 $\square$ II 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

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.

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.

Step 1: Given Information

We are given the following information:

Avenue $ A $ is parallel to Avenue $ B $.
Avenue $ A $ is perpendicular to Main Street.

Step 2: Determine the Relationship

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.

Step 3: Apply the Perpendicular Transversal Theorem

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

Final Answer

The correct answer is: \[ \boxed{\text{Avenue B and Main Street will be perpendicular by the Perpendicular Transversal Theorem since Avenue A is parallel to Avenue B.}} \]

The answer is $\boxed{\text{A}}$.

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