Question

problem 20: (first taught in lesson 29) select the converse of this statement, and determine whether it is true or false. if a triangle is obtuse, then it has (at least) one angle that is less than 90°.

Explanation:

Step1: Define converse

Switch hypothesis and conclusion.
Original: If $p$ (triangle is obtuse) then $q$ (has angle < 90°). Converse: If $q$ then $p$.

Step2: Analyze truth - value

A triangle with one angle less than 90° can be acute (all angles < 90°) or right - angled (one 90° angle), not necessarily obtuse. So false.

Answer:

The converse statement: If a triangle has (at least) one angle that is less than 90°, then it is obtuse. False.