Let's break down the problem:

1. Original statement: "If a figure is a square (p), then its diagonals divide it into isosceles triangles (q)."

   • This is represented as $p \rightarrow q$.

2. Converse of the statement: The converse of $p \rightarrow q$ is $q \rightarrow p$, which translates to: "If a figure's diagonals divide it into isosceles triangles (q), then the figure is a square (p)."

3. Truth of the converse:

   • The converse $q \rightarrow p$ is false. While squares do have diagonals that divide them into isosceles triangles, other figures like rectangles and rhombuses also have this property. Thus, the converse is not always true.

Correct Answers:

• $q \rightarrow p$
• The converse of the statement is false.

Do you want more details or have any questions?

Here are five related questions to consider:

1. What does it mean for two statements to be logically equivalent?
2. Can you provide an example where $q$ is true, but $p$ is false?
3. How would you represent the inverse of the original statement?
4. What is the contrapositive of the original statement?
5. Are there other geometric figures where the diagonals divide them into isosceles triangles?

Tip: When evaluating the truth of a converse statement, consider counterexamples where the hypothesis holds, but the conclusion does not.