Write the following statement as a biconditional:
If two angles are vertical angles, then they are congruent
A Two angles are vertical angles if and only if they are congruent.
B Two angles are vertical angles if and only if they are congruent.
C If two angles are congruent, then they are vertical angles
D If two angles are not vertical angles, then they are not congruent
B Two angles are vertical angles if and only if they are congruent.
B Two angles are vertical angles if and only if they are congruent.
The correct biconditional statement for the given statement "If two angles are vertical angles, then they are congruent" is:
B) Two angles are vertical angles if and only if they are congruent.
To understand how we arrive at this answer, let's break it down further:
In the original statement, we have two parts: the condition and the conclusion. The condition is "two angles are vertical angles," and the conclusion is "they are congruent."
To form the biconditional statement, we need to combine these two parts using the phrase "if and only if" (abbreviated as "iff").
So, the biconditional statement can be written as: "Two angles are vertical angles if and only if they are congruent."
Option B correctly represents this biconditional statement.