Question

Explain how corollary 1 follows from theorem 4-1 such that an equilateral triangle is also equiangular.

Short answer

An equilateral triangle is also equiangular.

Step-by-step solution

Step 1. Consider the figure.

Consider the figure of equilateral triangle.

Step 2. Apply the concept of isosceles triangles.

Equiangular: when all the interior angles are equal in measure or say all angles are congruent, then the figure is said to be equiangular.

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.$\overline{AB}\cong \overline{AC}$	From the figure
2.$\angle B\cong \angle C$	Isosceles theorem
3.$\overline{AB}\cong \overline{BC}$	From the figure
4.$\angle C\cong \angle A$	Isosceles theorem
5.$\overline{CA}\cong \overline{BC}$	From the figure
6.$\angle A\cong \angle B$	Isosceles theorem
7.$\angle A\cong \angle B\cong \angle C$	Transitive property
8.$\mathrm{\Delta }ABC$ is equiangular	Definition of equiangular

Thus, the above proof shows that how corollary 1 follows from the Isosceles triangle theorem.