Chapter 4.6, Problem 36PPS

To determine

To Prove:

Corollary $4.4$ .

Explanation of Solution

Proof:

Equilateral triangle corollary states that “each angle of an equilateral triangle measures $60$ ”.

It is given that,

  $△ABC$ Is equilateral.

  

  $m\angle A=60,m\angle B=60,m\angle C=60$

Statements	Reasons
$△ABC$ is equiangular	Given
$△ABC$ is equiangular	An equilateral triangle is equiangular
$\angle A\cong \angle B\cong \angle C$	Definition of equiangular triangle.
$m\angle A+m\angle B+m\angle C=180$	Triangle angle-sum theorem
$3\left(m\angle A\right)=180$	Substitution.
$m\angle A=60$	Multiplication property
$m\angle A+m\angle B+m\angle C=60$	Substitution