Question
Question 4(Multiple Choice Worth 1 points)
(01.05 MC)
Jenni wrote a conditional statement and its converse.
Conditional: If angles are right angles, then the angles have the same measure.
Converse: If angles have the same measurement, then they are right angles.
Did Jenni write the converse statement properly? Determine if the converse is true or false and give a counterexample if the converse is false.
No; two angles that each measure 45°
Yes; two angles that each measure 90°
Yes; two angles that each measure 41°
No; two angles that each measure 82°
(01.05 MC)
Jenni wrote a conditional statement and its converse.
Conditional: If angles are right angles, then the angles have the same measure.
Converse: If angles have the same measurement, then they are right angles.
Did Jenni write the converse statement properly? Determine if the converse is true or false and give a counterexample if the converse is false.
No; two angles that each measure 45°
Yes; two angles that each measure 90°
Yes; two angles that each measure 41°
No; two angles that each measure 82°
Answers
GPT-4o mini
To determine whether Jenni wrote the converse statement correctly, we can analyze both the original conditional statement and its converse.
1. **Original Conditional**: "If angles are right angles, then the angles have the same measure."
- This statement is true, as right angles always measure 90 degrees.
2. **Converse**: "If angles have the same measurement, then they are right angles."
- This statement is not necessarily true. Angles can have the same measurement and not be right angles.
To provide a counterexample:
- Consider two angles that each measure 45°. They have the same measurement (45°) but are not right angles (which measure 90°).
Given this analysis, we can conclude:
- Jenni did **not** write the converse statement properly because it is false.
- The counterexample is: **No; two angles that each measure 45°**.
So, the correct answer is:
**No; two angles that each measure 45°.**
1. **Original Conditional**: "If angles are right angles, then the angles have the same measure."
- This statement is true, as right angles always measure 90 degrees.
2. **Converse**: "If angles have the same measurement, then they are right angles."
- This statement is not necessarily true. Angles can have the same measurement and not be right angles.
To provide a counterexample:
- Consider two angles that each measure 45°. They have the same measurement (45°) but are not right angles (which measure 90°).
Given this analysis, we can conclude:
- Jenni did **not** write the converse statement properly because it is false.
- The counterexample is: **No; two angles that each measure 45°**.
So, the correct answer is:
**No; two angles that each measure 45°.**