Let's break down the questions one by one.

1. Vocabulary

The statement given is: "If a triangle is equilateral, then it is isosceles."

• This type of statement is called a conditional statement.
• The term being asked for here is the hypothesis or the antecedent, which is the part of the statement that comes after "if".
• The answer is hypothesis.

2. Converse of the Conditional Statement

The given statement is: "If I drink enough water, I am not dehydrated."

• The converse of a conditional statement is formed by switching the hypothesis and the conclusion.
• So, the converse would be: "If I am not dehydrated, then I drink enough water."

3. For a Polygon, Which Statement is True?

Let's analyze each option:

• A: "If a polygon is irregular, then it is not equilateral."

  • This is true. An irregular polygon has sides of different lengths, so it cannot be equilateral (where all sides are equal).

• B: "If a polygon is irregular, then it is not equiangular."

  • This is not always true. A polygon can be irregular but still equiangular (like a rectangle, which has all angles equal but not all sides).

• C: "If a polygon is not equilateral, then it is irregular."

  • This is false. A polygon can be equiangular but not equilateral, like a rectangle.

• D: "If a polygon is equiangular, then it is equilateral."

  • This is false. An example is a rectangle, which is equiangular but not equilateral unless it's a square.

The correct answer is A.

Would you like more details on any of these questions or explanations?

Here are 5 related questions for further exploration:

1. What is the contrapositive of a conditional statement?
2. How do you determine if a polygon is regular or irregular?
3. What is the biconditional statement, and how is it formed?
4. Can you give an example of a polygon that is equilateral but not equiangular?
5. What is the difference between sufficient and necessary conditions in logical statements?

Tip: When forming the converse of a statement, remember to swap the "if" and "then" parts to ensure clarity and correctness.