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I see you've uploaded an image. Let me analyze it to provide further assistance.The image contains a multiple-choice question on the law of deductive reasoning, particularly focusing on triangles. Here’s the key part of the question visible in the image:

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**"What law of deductive reasoning is being used? (1 point)"**

- If a triangle is equilateral, then its three sides are congruent.
- Triangle ABC is equilateral, so its three sides are congruent.
- Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

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The options below the question include:

1. Law of Detachment
2. Law of Syllogism
3. Law of Subtraction (partial visibility, likely incorrect option)
4. Law of Something (hard to read)

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The law of deductive reasoning being used in this example is the **Law of Detachment**. This law states that if a conditional statement ("If P, then Q") is true, and P is true, then Q must also be true.

In this case:
- Premise: "If a triangle is equilateral, then its sides are congruent."
- Given: "Triangle ABC is equilateral."
- Conclusion: "Therefore, the sides of triangle ABC are congruent."

This follows the Law of Detachment.

Would you like a further explanation of deductive reasoning, or how this law applies to other problems?

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Here are 5 related questions to deepen your understanding:

1. What is the difference between the Law of Detachment and the Law of Syllogism?
2. Can the Law of Detachment be used in non-geometric contexts?
3. How would you identify a deductive reasoning law from a more complex set of premises?
4. In what real-life situations can deductive reasoning help with problem-solving?
5. What are some common misconceptions about the Law of Detachment?

**Tip:** Always ensure that the "if-then" structure in deductive reasoning is logically valid before drawing conclusions.

What law of deductive reasoning is being used? If a triangle is equilateral, then its three sides are congruent. Triangle ABC is equilateral, so its three sides are congruent. Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

Explore the Law of Detachment through the example of triangle properties. Understand how deductive reasoning is applied in this geometry problem involving equilateral triangles. This problem is suitable for students in Grades 9-12.

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