Question 4(Multiple Choice Worth 1 points)

Question

(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°

Answer 1

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°.