Question

Explain how corollary 2 follows from corollary such that an equilateral has three 60-degree angles.

Short answer

An equilateral triangle has three 60-degree angles.

Step-by-step solution

Step 1. Consider the figure.

Consider the figure of equilateral triangle.

Step 2. Apply the concept of isosceles triangles.

Corollary 1: An equilateral triangle is also equiangular.

Corollary 2: An equilateral triangle has three 60-degree angles.

The Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

Step 3. Step description.

From the figure, $\mathrm{\Delta }ABC$is equilateral such that $\overline{AB}\cong \overline{BC}\cong \overline{CA}$.

Statements	Reasons
1.$\overline{AB}\cong \overline{AC}$	is equilateral
2.$\angle A\cong \angle B\cong \angle C$	Corollary 1
3.$m\angle A=m\angle B=m\angle C$	Definition of congruent angles
4.$m\angle A=m\angle B=m\angle C=180°$	Sum of angles of a triangle is
5.$$\begin{gathered} m\angle A+m\angle A+m\angle A=180° \\ 3\times m\angle A=180° \\ m\angle A=\frac{180°}{3}=60° \end{gathered}$$	Substitution property
6. Similarly,$m\angle B=m\angle C=60°$	From the previous step

Thus, the above proof above shows that how Corollary 2 follows from Corollary 1.