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

Question

Responses

obtuse equilateral
obtuse equilateral

right equilateral
right equilateral

equilateral scalene
equilateral scalene

right isosceles

Answer 1

To determine the possible types of triangles based on the Triangle Inequality Theorem, let's analyze the options:

1. Obtuse Equilateral: An equilateral triangle cannot be obtuse because each angle in an equilateral triangle is exactly 60 degrees. Therefore, this type of triangle is not possible.

2. Right Equilateral: Similar to the above, an equilateral triangle cannot be a right triangle since all angles must sum to 180 degrees, and if one angle is 90 degrees, the other two cannot be 60 degrees. This type is also not possible.

3. Equilateral Scalene: An equilateral triangle, by definition, has all sides equal and all angles equal (60 degrees each), meaning it cannot be scalene, which requires all sides (and angles) to be different. Therefore, this type is not possible.

4. Right Isosceles: A right isosceles triangle has one right angle (90 degrees) and the other two angles are equal, meaning that they both measure 45 degrees. This is a valid type of triangle.

Based on this analysis, the only possible triangle type among the options listed is right isosceles.