https://file.aiquickdraw.com/mathbot/file/1728677671670gh7h9d0y.jpg

The image shows a worksheet with various geometry and logic-based questions. Let's go through the questions and provide solutions:

### 9. Write the contrapositive of the following statement:
**"If an angle is a right angle, then it is not acute."**
- Contrapositive: "If an angle is acute, then it is not a right angle."

### 10. Which statement has the same truth value as the given statement?
- Answer: The contrapositive of any statement always has the same truth value. Therefore, the contrapositive from question 9 is the answer.

### 11. What can be concluded from the statement "m∠1 + m∠2 = 180°"?
- Answer: **C**. ∠1 and ∠2 are supplementary (two angles are supplementary if their measures sum to 180°).

### 12. Which is a counterexample for the biconditional: "An angle measures 80 degrees if and only if the angle is acute"?
- Answer: **D**. m∠90°. This is a counterexample because an angle of 90° is acute by some standards but not less than 90°, breaking the "if and only if" condition.

### 13. Which conditional can be used to write a true biconditional?
- Answer: **D**. If two angles are supplementary, then they are not congruent. This can form a true biconditional because it's reversible as both statements are true.

### 14. Give an example of the symmetric property of equality.
- Example: If a = b, then b = a. Any true equality between two terms, like "If x = 7, then 7 = x", shows symmetry.

### 15. Lilly conjectures that a number is divisible by 15, then it's also divisible by 5. Give a counterexample.
- A counterexample is not possible here since the conjecture is true. If a number is divisible by 15, it is necessarily divisible by both 3 and 5 (since 15 = 3 × 5).

### 16. Use the Law of Detachment below:
**"If Cameron scores greater than 75 on his test, he earns a B. Cameron scores an 81 on his test."**
- Conclusion: Cameron got a B. (This follows directly from the Law of Detachment.)

### 17. Use the Law of Syllogism to complete the conclusion:
**"If it’s raining, then the sidewalk will be wet. If the sidewalk is wet, then the sidewalk will be slippery."**
- Conclusion: **"If it’s raining, then the sidewalk will be slippery."** (This is the Law of Syllogism: if A → B and B → C, then A → C.)

### 18. What is inductive reasoning?
- Answer: **"Making generalizations based on specific observations."** This type of reasoning involves drawing conclusions from patterns or examples.

---

Do you want details or explanations on any of the answers? 

Here are 5 related questions to practice:
1. What is the converse of the statement: "If an angle is acute, then it is less than 90 degrees"?
2. Write the inverse of the statement: "If a number is divisible by 10, then it is divisible by 2."
3. How does the Law of Detachment differ from the Law of Syllogism?
4. Can an angle of 90° be considered acute in any context? Explain.
5. What is the contrapositive of "If it rains, then I will take an umbrella"?

**Tip:** The contrapositive of a statement always has the same truth value as the original statement.

Write the contrapositive of the following statement: 'If an angle is a right angle, then it is not acute.'

Learn how to write the contrapositive of a given conditional statement in geometry, such as 'If an angle is a right angle, then it is not acute.' This exercise is important for understanding logical relationships in geometry and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation