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The conditional statement given is:

**"If two lines intersect at right angles, then the two lines are perpendicular."**

To break this down:

- **Hypothesis (the "if" part)**: This is the assumption or condition of the statement. In this case, the hypothesis is **"Two lines intersect at right angles."**
- **Conclusion (the "then" part)**: This is the result or outcome if the hypothesis is true. In this case, the conclusion is **"The two lines are perpendicular."**

Now, let's examine the options:

- **a.** The hypothesis and conclusion are reversed.
- **b.** This correctly identifies the hypothesis as **"Two lines intersect at right angles"** and the conclusion as **"The two lines are perpendicular."**
- **c.** This is incorrect as it introduces a statement that contradicts the conditional statement.
- **d.** This is also incorrect because it reverses the logical structure and introduces a false conclusion.

Thus, the correct answer is **b**.

Would you like further clarification or more details on this?

Here are some related questions for further practice:

1. What is the contrapositive of the given conditional statement?
2. What is the converse of the conditional statement?
3. How can the hypothesis and conclusion of a statement be symbolized in logic?
4. How does the definition of perpendicular lines relate to right angles?
5. How do you form a biconditional statement from a given conditional statement?

**Tip:** In conditional statements, the hypothesis comes after the "if" and the conclusion follows the "then."

Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular.

Learn how to identify the hypothesis and conclusion in a conditional statement involving perpendicular lines. This problem is ideal for middle and high school students, focusing on geometric relationships and logical reasoning.

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