Question

Rewrite the definition of the term as a biconditional statement. Two angles are vertical angles when their sides form two pairs of opposite rays. If an angle is vertical to another angle, then the angles do not form pairs of opposite rays. If two angles are vertical, then their sides form two pairs of opposite rays. An angle is vertical to another angle if and only if the angles do not form pairs of opposite rays. Two angles are vertical angles if and only if their sides form two pairs of opposite rays.

Answer 1

D. Two angles are vertical angles if and only if their sides form two pairs of opposite rays

Explanation:

A conditional statement is a statement that is is not truely ascertain except a particular condition is also true. This is done by using an IF statement. When a statement is biconditional, it means it is combined form of a conditional statement. The later is written by combining "two ifs" i.e IF and only IF. The statement is trying to ascertain two conditional statements at a time.

Given the statement "Two angles are vertical angles when their sides form two pairs of opposite rays.", we can see that it is made up to two statements.

1) Two angles are vertical angles

2) their sides form two pairs of opposite rays.

To ascertain the truthfulness of both statements, we will use the biconditional statement " if and only if". Hence the statement will become "Two angles are vertical angles if and only if their sides form two pairs of opposite rays"

Hence, option D is correct