Let's analyze the given statements:
Statement 1: A triangle is equilateral if and only if it has three congruent sides.
- This tells us that a triangle being equilateral is equivalent to it having three congruent sides. This is a biconditional statement, meaning both the "if" and the "only if" parts are true.
Statement 2: A triangle has three congruent sides if and only if it is equilateral.
- This is essentially the converse of Statement 1. The converse of a biconditional statement swaps the "if" and "only if" parts. However, since Statement 1 is a biconditional statement, its converse will also be true, making Statement 2 also true.
So, when asked about whether Statement 2 is true or false:
- Statement 2 is "true"
Next, we analyze the general nature of a biconditional statement and its converse.
- A biconditional statement is true if both directions of the implication are true. Its converse is simply the original statement because a biconditional statement reads the same forwards and backwards.
Therefore:
- The converse of a biconditional statement is "true"
Putting it all together:
Statement 2 is "true". The converse of a biconditional statement is "true".
