Question

problem 5: (first taught in lesson 43) complete this sentence with the best of the choices given. a triangle is equilateral iff it is ________.

Explanation:

Step1: Recall triangle properties

An equilateral triangle has all sides equal. By the converse of the base - angles theorem (in a triangle, if sides are equal, then the angles opposite them are equal), an equilateral triangle has all angles equal. Also, if a triangle has all angles equal (equiangular), then by the law of sines ($\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$), all sides are equal.

Answer:

A triangle is equilateral iff it is equiangular.