Question

Can an equilateral triangle be a right triangle?

Answer 1

Never.

Explanation:

An equilateral triangle has all angles equal to 60 degrees. For a right triangle one angle has to be 90 degrees.

Answer 2

Only if it's a curvilinear triangle - e.g. on the surface of a sphere.

Explanation:

Normally the angles of a triangle add up to `180^@`, so the angles of an equilateral triangle will all be `60^@`

The angles of a curvilinear triangle on the surface of a sphere always add up to more than `180^@`.

Imagine a triangle with one side running along the equator, one quarter of the way round the sphere and the other two sides running from the ends of that side to meet at the North pole. This will have three angles of `90^@`.