Question

problem 21: decide whether this definition passes the reversibility test by writing its converse and determining whether the converse is true. then, select the correct answer. if a triangle is obtuse, then it has three sides.

Explanation:

Step1: Write the converse

The original statement is "If a triangle is obtuse, then it has three sides." The converse is formed by switching the hypothesis and conclusion, so it is "If a triangle has three sides, then it is obtuse."

Step2: Evaluate the truth of the converse

A triangle is defined as a three - sided polygon. There are different types of triangles such as acute (all angles less than 90°), right - angled (one angle equal to 90°), and obtuse (one angle greater than 90°). Just because a triangle has three sides does not mean it is obtuse. So the converse is false. Since the converse is false, the original definition does not pass the reversibility test.

Answer:

The converse is "If a triangle has three sides, then it is obtuse." The converse is false because a triangle with three sides can be acute, right - angled, or obtuse. So the definition does not pass the reversibility test.