no
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No. In an equilateral triangle, all three angles are the same. Since they are not ninety degrees, you can't have a right triangle that is also an equilateral triangle.
no. an equilateral triangle is also equiangular, so the angles are 60 degrees each. a right triangle cannot be equilateral
In the geometry of triangles, there is no such thing as stability.
It can be scalene or isosceles but not equilateral.