Which biconditional is not a good definition?
A whole number is odd if and only if the number is not divisible by 2.
• An angle is straight if and only if its measure is 180°
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A whole number is even if and only if it is divisible by 2.
A ray is a bisector of an angle if and only if it splits the angle into two angles.
The biconditional "A ray is a bisector of an angle if and only if it splits the angle into two angles" is not a good definition.
The biconditional "A whole number is odd if and only if the number is not divisible by 2" is not a good definition.
The biconditional that is not a good definition is "An angle is straight if and only if its measure is 180°."
To determine the incorrect biconditional, we need to understand the meaning and conditions of each statement. A biconditional is a statement that links two conditions together, stating that one condition is true if and only if the other condition is true.
Let's analyze each option to find the incorrect one:
1. "A whole number is odd if and only if the number is not divisible by 2."
This biconditional is correct. An odd number is exactly defined as a number that cannot be divided evenly by 2.
2. "An angle is straight if and only if its measure is 180°."
This biconditional is not a good definition because it wrongly suggests that any angle measuring 180° is straight. However, an angle measuring 180° can also be a full circle. Thus, not all angles measuring 180° are necessarily straight.
3. "A whole number is even if and only if it is divisible by 2."
This biconditional is correct. An even number is defined as a number that can be divided evenly by 2.
4. "A ray is a bisector of an angle if and only if it splits the angle into two angles."
This biconditional is correct. A bisector of an angle splits the angle into two equal angles, and any ray satisfying this condition is a bisector.
Therefore, the biconditional "An angle is straight if and only if its measure is 180°" is not a good definition, as explained above.