Question

Park street is parallel to Rock street. Garden street is perpendicular (90°) to Lake street. Lake street is parallel to Rock street. For the situation described above, the TRUE statement is

• A. Park street is perpendicular to Lake street
• B. Rock street is parallel to Garden street
• C. Park street is parallel to Garden street
• D. Garden street is perpendicular to Park street

Hint:

In problems involving geometry and spatial relationships, carefully analyze the given relationships to deduce perpendicular and parallel lines.

Answer 1

The Correct Option is A, D

Step 1: Understanding the given relationships.
- Park street is parallel to Rock street.
- Garden street is perpendicular (90°) to Lake street.
- Lake street is parallel to Rock street.
From these relationships, we can deduce:
- Since Rock street is parallel to both Park and Lake streets, Park street and Lake street must be perpendicular to each other. Therefore, statement (A) is true.
- Since Garden street is perpendicular to Lake street, and Lake street is parallel to Rock street, Garden street must also be perpendicular to Park street. This confirms that (D) is also true.

Step 2: Analyzing the other options.
- (B) Rock street is parallel to Garden street: This is not necessarily true based on the given information.
- (C) Park street is parallel to Garden street: This is not true since Garden street is perpendicular to Lake street, and hence must be perpendicular to Park street as well.

Step 3: Conclusion.
The correct answers are (A) and (D), as they correctly describe the geometric relationships between the streets.