Which of the following statements is never true?
a. a right triangle is equilateral.
b. a right triangle is isosceles.
c. an acute triangle is equilateral.
d. an acute triangle is isosceles.

A.
Never true. The angles of an equilateral triangle are 60° each, so an equilateral triangle can never be a right triangle which has one angle 90°.

b.
Possible. An isosceles right triangle has angles 45°, 45°, 90°.

c.
Possible. The angles of an equilateral triangle are 60° each, so it's always an acute triangle.

d.
Possible. For example a triangle with angles 70°, 70°, 40° - the angles are less than 90°, so they are all acute, and there are two angles with the same measure, so it's an isosceles triangle.

The answer is A.