Question

Determine whether the following definition is reversible (both true as conditional and converse). If it is, which statement below is the correct bi-conditional? *

A. The statement is not reversible.
B. If two angles are congruent, then they have equal measure
C. If two angles have the same measure, then they are congruent.
D. Two angles are congruent if and only if they have equal measure.

Answer 1

The definition that 'Two angles are congruent if and only if they have equal measure' is reversible and correctly represents a biconditional statement where having the same measure is both necessary and sufficient for two angles to be congruent.

Step-by-step explanation:

The definition in question is indeed reversible, meaning it holds true in both the conditional and converse forms. When we say that two angles are congruent, we mean that they have the same measure. Conversely, if two angles have the same measure, then they are indeed congruent. This relationship is an example of a necessary and sufficient condition, as having the same measure is both necessary and sufficient for two angles to be congruent.

The correct bi-conditional statement combining these two conditions is option D: 'Two angles are congruent if and only if they have equal measure.' This statement indicates that having equal measures is both required and enough for two angles to be congruent, satisfying the criteria for a reversible definition.