Based on the Triangle Inequality Theorem, which of the following types of triangles is possible?(1 point)

Question

Responses

equilateral scalene
equilateral scalene

obtuse equilateral
obtuse equilateral

right isosceles
right isosceles

right 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.

Now, let's analyze each option:

1. Equilateral scalene: This is a contradiction because an equilateral triangle (all sides equal) cannot be scalene (all sides different). Hence, this type is not possible.

2. Obtuse equilateral: An equilateral triangle cannot be obtuse since all angles in an equilateral triangle are 60 degrees. So, this type is also not possible.

3. Right isosceles: A right triangle can indeed be isosceles (two sides equal and one angle measuring 90 degrees). Thus, this type is possible.

4. Right equilateral: Similar to the obtuse equilateral, an equilateral triangle cannot be right-angled as all angles must be 60 degrees. So, this type is not possible.

Based on this analysis, the only type of triangle that is possible according to the Triangle Inequality Theorem is right isosceles.