Based on the Triangle Inequality Theorem, which of the following types of triangles is possible?(1 point) Responses equilateral scalene equilateral scalene right equilateral right equilateral right isosceles right isosceles obtuse equilateral

Answer 1

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Based on this theorem, all types of triangles mentioned in your list are possible:

1. Equilateral: All sides are equal, so the sum of any two sides will always equal the third side.
2. Scalene: All sides are of different lengths, and as long as they adhere to the triangle inequality, they can form a triangle.
3. Right: A right triangle can also adhere to the triangle inequality, for example, sides of lengths 3, 4, and 5 fulfill both the Pythagorean theorem and the triangle inequality.
4. Isosceles: Similar to scalene, as long as the side lengths adhere to the triangle inequality, an isosceles triangle is possible.
5. Obtuse: An obtuse triangle can also be formed as it fulfills the triangle inequality.

Therefore, all the types of triangles you listed are possible.