Geometry 2-3 (Biconditionals and Definitions)

How can you combine the following statements as a biconditional? If this month is June, then next month is July. If next month is July, then this month is June.

• This month is June if and only if the next month is July.

• The next month is July if and only if this month is June.

• If this month is July, then the previous month was June.

• This month is July if and only if the previous month was June.

Write the following definition as a biconditional. Vertical angles are two angles whose sides are opposite rays.

• If two angles are across from each other, then they are vertical.

• If two angles have sides that are opposite rays, then they are vertical angles.

• If two angles are vertical, then they have sides with opposite rays.

• Two angles are vertical if and only if their sides are opposite rays.

Is the following a good definition? Elephants are gigantic animals.

• Yes

• No, because elephants are not gigantic.

• No, because it is not written as a biconditional statement.

• No, because the converse of the conditional statement is false.