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I see that you've uploaded a worksheet focused on writing the converse, inverse, and contrapositive of logical statements. Let's go through it step by step to make sure you understand the concepts and verify your answers.

### Key concepts:
1. **Converse**: Switch the hypothesis and conclusion.
2. **Inverse**: Negate both the hypothesis and conclusion.
3. **Contrapositive**: Switch and negate both the hypothesis and conclusion.

I'll address the statements from your worksheet.

### Statement 1:
- **Given**: If two angles are adjacent angles, then they are complementary.
  - **Converse**: If two angles are complementary, then they are adjacent angles.
  - **Inverse**: If two angles are not adjacent, then they are not complementary.
  - **Contrapositive**: If two angles are not complementary, then they are not adjacent angles.

### Statement 2:
- **Given**: If two angles are congruent, then the two angles are right angles.
  - **Converse**: If two angles are right angles, then the two angles are congruent.
  - **Inverse**: If two angles are not congruent, then the two angles are not right angles.
  - **Contrapositive**: If two angles are not right angles, then they are not congruent.

Now, looking at the truth values and counterexamples part of the worksheet (below the logical transformations), it appears you need to determine whether these statements are true or false and provide a counterexample if false.

Would you like me to help you further verify truth values or provide counterexamples?

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Here are 5 related questions to deepen understanding:
1. What is the difference between a statement's contrapositive and its inverse?
2. Can you think of a real-life example where a contrapositive would be useful?
3. How would you determine whether the converse of a statement is always true?
4. How do counterexamples disprove mathematical statements?
5. Why is the contrapositive of a true statement always true?

**Tip**: For conditional statements, always remember that if the contrapositive is true, then the original statement must also be true!

Write the converse, inverse, and contrapositive for the given statement: 'If two angles are adjacent angles, then they are complementary.' Determine the truth value for each form.

Learn how to find the converse, inverse, and contrapositive of conditional statements in geometry, with a detailed example involving adjacent and complementary angles. Suitable for high school students in Grades 9-10.

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