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https://math.answers.com/math-and-arithmetic/Can_a_right_triangle_also_be_isosceles_or_equilateral_why

Can a right triangle also be isosceles or equilateral why? - Answers

"It can be isosceles but not equilateral. Since a property of an equilateral triangle is having all angles equal (hence all sides equal), having one right angle changes that. The angles would be 90, some alpha, and some beta (not equal). Having the angles 90, 45, and 45 renders it an isosceles triangle." This is all well and correct -- for a triangle in a plane. But if your triangle is on a different surface, then you can indeed have an equilateral right triangle. If the triangle is on a sphere, for example, you can have right angles at three different points, each a quarter of the circumference from each other, and the resulting triangle (with sides that we would perceive as curved) would also be equilateral.



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Can a right triangle also be isosceles or equilateral why? - Answers

https://math.answers.com/math-and-arithmetic/Can_a_right_triangle_also_be_isosceles_or_equilateral_why

"It can be isosceles but not equilateral. Since a property of an equilateral triangle is having all angles equal (hence all sides equal), having one right angle changes that. The angles would be 90, some alpha, and some beta (not equal). Having the angles 90, 45, and 45 renders it an isosceles triangle." This is all well and correct -- for a triangle in a plane. But if your triangle is on a different surface, then you can indeed have an equilateral right triangle. If the triangle is on a sphere, for example, you can have right angles at three different points, each a quarter of the circumference from each other, and the resulting triangle (with sides that we would perceive as curved) would also be equilateral.



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https://math.answers.com/math-and-arithmetic/Can_a_right_triangle_also_be_isosceles_or_equilateral_why

Can a right triangle also be isosceles or equilateral why? - Answers

"It can be isosceles but not equilateral. Since a property of an equilateral triangle is having all angles equal (hence all sides equal), having one right angle changes that. The angles would be 90, some alpha, and some beta (not equal). Having the angles 90, 45, and 45 renders it an isosceles triangle." This is all well and correct -- for a triangle in a plane. But if your triangle is on a different surface, then you can indeed have an equilateral right triangle. If the triangle is on a sphere, for example, you can have right angles at three different points, each a quarter of the circumference from each other, and the resulting triangle (with sides that we would perceive as curved) would also be equilateral.

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      "It can be isosceles but not equilateral. Since a property of an equilateral triangle is having all angles equal (hence all sides equal), having one right angle changes that. The angles would be 90, some alpha, and some beta (not equal). Having the angles 90, 45, and 45 renders it an isosceles triangle." This is all well and correct -- for a triangle in a plane. But if your triangle is on a different surface, then you can indeed have an equilateral right triangle. If the triangle is on a sphere, for example, you can have right angles at three different points, each a quarter of the circumference from each other, and the resulting triangle (with sides that we would perceive as curved) would also be equilateral.

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