Question

problem 21: select the converse of this statement and determine whether it is true or false. if a triangle is equilateral, then it is also equiangular.

Explanation:

Step1: Define converse

Switch hypothesis and conclusion.
Original: If $A$ (triangle is equilateral), then $B$ (triangle is equiangular). Converse: If $B$, then $A$.

Step2: Recall geometric property

In Euclidean geometry, an equiangular triangle has all angles equal ($60^{\circ}$ each). By the law of sines $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$, when $A = B=C = 60^{\circ}$, we have $a=b = c$, so it is equilateral.

Answer:

The converse statement is "If a triangle is equiangular, then it is equilateral" and it is true.