Question

Explain how corollary follows from theorem 4-2.

Short answer

An equilateral triangle is also equiangular the two angles are congruent, then the sides opposite to those angles are congruent.

Step-by-step solution

Step 1. Consider the figure.

Consider the figure.

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 angles are congruent, then the sides opposite to those angles are congruent. Corollary 1: An equilateral triangle is also equiangular.

Theorem 4-2, Two angles are congruent, then the sides opposite to those angles are congruent

Step 3. Step description.

Use the two-column form as follows:

Statements	Reasons
1.$\mathrm{\Delta }ABC$ is equiangular	From the statement
2.$\angle A\cong \angle C$	Definition of equiangular triangle
3.$\overline{AB}\cong \overline{BC}$	Converse of isosceles theorem
4.$\angle B\cong \angle C$	Definition of equiangular triangle
5.$\overline{AB}\cong \overline{AC}$	Converse of isosceles theorem
6.$\angle A\cong \angle B$	Definition of equiangular triangle
7.$\overline{BC}\cong \overline{AC}$	Converse of isosceles theorem
8.$\overline{AB}\cong \overline{BC}\cong \overline{AC}$	Transitive property
9.$\mathrm{\Delta }ABC$ is equilateral	Definition of equilateral

Thus, the above proof shows that how Corollary follows from the converse of isosceles triangle theorem.