Question

PLEASE HELP!! Rewrite the definition of the term as a biconditional statement... Two angles are vertical angles when their sides form two pairs of opposite rays.

A. Vertical angles are formed when two pairs of opposite rays share the same sides.
B. If two angles are vertical angles, then their sides form two pairs of opposite rays.
C. Two angles forming two pairs of opposite rays are always vertical angles.
D. Vertical angles exist only when two pairs of opposite rays intersect.

Answer 1

Option B is the correct biconditional statement defining vertical angles: 'If two angles are vertical angles, then their sides form two pairs of opposite rays.' This statement satisfies the condition for a biconditional by being reversible.

Step-by-step explanation:

The question asks to rewrite the definition of vertical angles as a biconditional statement. A biconditional statement is one where both parts imply each other; essentially, the 'if' and 'only if' parts. The correct biconditional statement for vertical angles based on the given definition would be, 'Two angles are vertical angles if and only if their sides form two pairs of opposite rays.' This statement ensures that the definition works both ways, i.e., if two angles are vertical angles, then they have sides that form two pairs of opposite rays, and conversely, if two angles have sides that form two pairs of opposite rays, then they are vertical angles.

From the options provided, option B fits this definition: 'If two angles are vertical angles, then their sides form two pairs of opposite rays.' This statement can also be reversed, which would still hold true, fulfilling the condition for a biconditional statement.