https://file.aiquickdraw.com/mathbot/file/17267593632281wra89fy.jpg

Let's go through the statements one by one based on the diagram and evaluate them:

1. **\( \overrightarrow{BE} \) and \( \overrightarrow{IF} \) are perpendicular.**
   - Looking at the diagram, line \( BE \) is horizontal, and line \( IF \) is vertical. Therefore, these lines intersect at a 90-degree angle, making them perpendicular. 
   - **Answer: Yes**

2. **\( \angle HCD \) and \( \angle ICH \) are adjacent angles.**
   - \( \angle HCD \) is the angle formed by \( H \), \( C \), and \( D \), while \( \angle ICH \) is formed by \( I \), \( C \), and \( H \). These two angles share the common ray \( CH \) and have a common vertex at \( C \), meaning they are adjacent.
   - **Answer: Yes**

3. **\( \overrightarrow{CE} \) and \( \overrightarrow{CF} \) are opposite rays.**
   - \( \overrightarrow{CE} \) points to the left from \( C \) to \( E \), while \( \overrightarrow{CF} \) points to the right from \( C \) to \( F \). Since they extend in exactly opposite directions from point \( C \), they are opposite rays.
   - **Answer: Yes**

4. **\( \angle BCG \) and \( \angle DCF \) are congruent.**
   - \( \angle BCG \) is the angle formed by points \( B \), \( C \), and \( G \), and \( \angle DCF \) is formed by points \( D \), \( C \), and \( F \). Without any specific markings or additional information indicating that these angles are congruent, we cannot conclude they are. They do not seem to have any symmetry or other reasons to be congruent based on the diagram alone.
   - **Answer: No**

### Final answers for the table:
1. Yes
2. Yes
3. Yes
4. No

Would you like further details or clarification on any step?

Here are 5 related questions to extend your understanding:
1. How do you determine whether two angles are adjacent or not?
2. What other ways can you verify if two angles are congruent besides visual inspection?
3. How can you confirm if two rays are opposite without relying on appearance?
4. How are perpendicular lines identified in geometry?
5. Can two adjacent angles also be complementary? Why or why not?

**Tip:** In geometry, adjacent angles always share a common side, while congruent angles have equal measures.

Evaluate the given geometry diagram to determine the correctness of the following statements about perpendicularity, adjacent angles, opposite rays, and congruent angles.

Solve geometry problems involving perpendicular lines, adjacent angles, opposite rays, and congruent angles with a detailed solution. Suitable for students in Grades 7-9.

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