Which biconditional is not a good definition
A: an angle is obtuse if and only if the measure is greater than 180
B: an angle is a right angle if and only if it’s measure is 90
C: an angle is acute if and only if it’s measure is between 0 and 90
D: two angles are congruent if and only if their measures are the same
Option A: an angle is obtuse if and only if the measure is greater than 180.
The biconditional that is not a good definition is option A: "An angle is obtuse if and only if the measure is greater than 180."
This statement is not a good definition because it is incorrect. An angle is actually defined as obtuse if its measure is greater than 90 and less than 180, not greater than 180.
To determine which biconditional is not a good definition, we need to evaluate each option:
A: "An angle is obtuse if and only if the measure is greater than 180." This is a valid definition because by definition, an obtuse angle has a measure greater than 90 but less than 180.
B: "An angle is a right angle if and only if its measure is 90." This is also a valid definition because by definition, a right angle has a measure of exactly 90.
C: "An angle is acute if and only if its measure is between 0 and 90." This is a valid definition because by definition, an acute angle has a measure greater than 0 but less than 90.
D: "Two angles are congruent if and only if their measures are the same." This is not a good definition because it is circular. Congruent angles are defined as angles that have the same measure, so saying that they are congruent if and only if their measures are the same is simply restating the definition.
Therefore, the biconditional that is not a good definition is option D, "Two angles are congruent if and only if their measures are the same."