Do the following statement and its converse form a biconditional that is true?

If a triangle has a right angle, then it is right.

The given statement is:  
**"If a triangle has a right angle, then it is right."**

### Converse:
To check if the statement and its converse form a biconditional, we first need to find the converse of the statement.

The converse is:  
**"If a triangle is right, then it has a right angle."**

### Biconditional:
A biconditional statement is true if both the original statement and its converse are true.

1. **Original statement**:  
"If a triangle has a right angle, then it is right."  
This statement is true because a triangle with a right angle is, by definition, a right triangle.

2. **Converse**:  
"If a triangle is right, then it has a right angle."  
This is also true, since a right triangle is defined as a triangle with exactly one right angle.

Since both the statement and its converse are true, we can combine them into a biconditional:  
**"A triangle has a right angle if and only if it is right."**

This biconditional is **true**.

Would you like more details, or have any questions?

Here are 5 related questions to expand on this:

1. What is a biconditional statement, and how is it formed?
2. Can you form a biconditional statement using other properties of triangles (e.g., equilateral triangles)?
3. What is the difference between a converse and an inverse of a statement?
4. How can a conditional statement be false, and what are examples of this?
5. In what cases does the converse of a statement not hold?

**Tip:** Always check both the original statement and its converse when forming biconditional statements. Both must be true for the biconditional to hold.

Explore the concept of biconditional statements in geometry through an example involving right triangles. Learn how to determine if a statement and its converse form a true biconditional. Suitable for high school students studying geometry.

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