The incorrect statement among the D option D. A triangle with three congruent angles is equilateral. Therefore , D. A triangle with three congruent angles is equilateral is correct .
This statement is false because while an equilateral triangle does have three congruent angles, the converse is not necessarily true.
Now, let's briefly discuss the other options:
A. A triangle with three congruent sides is equiangular.
This statement is true. In an equilateral triangle (all sides equal), each angle is also congruent, making the triangle equiangular.
B. The Isosceles Triangle Theorem can be applied to equilateral triangles.
This statement is true. The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are also congruent. In an equilateral triangle, all sides are congruent, so this theorem applies.
C. The measure of each angle of an equilateral triangle is 120°.
This statement is true. In an equilateral triangle, each angle is 60 degrees. The sum of the interior angles of any triangle is always 180 degrees, so 60° + 60° + 60° equals 180°.