Which of the following is the contrapositive of ‘if two triangles are identical, then these are similar’?

Question 28Answer

a.

If two triangles are not identical, then these are similar.

b.

If two triangles are not similar, then they are not identical

c.

If two triangles are not similar, then these are identical.

d.

If two triangles are not identical, then these are not similar.

The contrapositive of a statement is formed by reversing and negating both the hypothesis and the conclusion. The original statement is:

**"If two triangles are identical, then these are similar."**

Let's break this down:
- **Original Statement:** If \( P \), then \( Q \).
- \( P \): Two triangles are identical.
- \( Q \): These triangles are similar.

The contrapositive of this statement would be:
- **Contrapositive:** If \( \neg Q \), then \( \neg P \).
- \( \neg Q \): Two triangles are not similar.
- \( \neg P \): These triangles are not identical.

Thus, the contrapositive is:

**"If two triangles are not similar, then they are not identical."**

This corresponds to option **b**.

So, the correct answer is:

**b. If two triangles are not similar, then they are not identical.**

Would you like more details on this concept or have any other questions? Here are some related questions:

1. What is the converse of the original statement?
2. How is a statement's inverse different from its contrapositive?
3. Can you explain the difference between similar and identical triangles?
4. What are some examples of statements where the contrapositive is useful?
5. How do you identify whether a statement is true or false based on its contrapositive?

**Tip:** In logic, the contrapositive of a true statement is always true.

Which of the following is the contrapositive of ‘if two triangles are identical, then these are similar’?

Explore the concept of contrapositive statements with a focus on triangles. This problem helps students understand how to form the contrapositive of a logical statement, specifically involving identical and similar triangles. Suitable for students in Grades 9-11.

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