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

Answer 1

To determine which types of triangles are possible based on the Triangle Inequality Theorem, we need to recall what the theorem states: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's analyze the given options:

1. Right Isosceles: This is a valid triangle. The sides can satisfy the triangle inequality.
2. Right Isosceles: Same as above; this is also valid.
3. Equilateral: This is valid as all sides are equal, and any two sides will always be greater than the third.
4. Scalene: This also can satisfy the triangle inequality as long as the side lengths are chosen correctly.
5. Equilateral: Same as above; valid.
6. Scalene: This is valid.
7. Obtuse Equilateral: Not possible, as an equilateral triangle cannot be obtuse (all angles are 60 degrees).
8. Obtuse Equilateral: Same as above; not possible.
9. Right Equilateral: Not possible, since an equilateral triangle cannot have a right angle.
10. Equilateral: Valid as mentioned earlier.

Based on this analysis, the types of triangles that are possible according to the Triangle Inequality Theorem are:

• Right Isosceles
• Equilateral
• Scalene

Thus, any combination of "right isosceles," "equilateral," and "scalene" triangles are possible, while "obtuse equilateral" and "right equilateral" are not possible options.