The biconditional statement given is: "A triangle is equilateral if and only if its three angles are congruent."
To form this biconditional statement, we need to combine a conditional statement with its converse. Let's break it down:
1. The given biconditional statement can be split into two parts:
- Part 1: "If a triangle is equilateral, then its three angles are congruent."
- Part 2: "If a triangle's three angles are congruent, then it is equilateral."
2. We need to identify a conditional statement and its converse that correspond to these parts. Here's an example:
- Conditional Statement: "If a triangle is equilateral, then its three angles are congruent."
- Converse: "If a triangle's three angles are congruent, then it is equilateral."
3. Therefore, the conditional statement that can be used with its converse to form the given biconditional statement is:
- "If a triangle is equilateral, then its three angles are congruent."
- Converse: "If a triangle's three angles are congruent, then it is equilateral."
By combining these two statements, we get the biconditional statement: "A triangle is equilateral if and only if its three angles are congruent."
