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

Question

Responses

right equilateral
right equilateral

right isosceles
right isosceles

equilateral scalene
equilateral scalene

obtuse equilateral

Answer 1

Based on the Triangle Inequality Theorem, let's analyze each option:

1. Right equilateral: This type is impossible because an equilateral triangle has all three sides equal, which does not satisfy the conditions for a right triangle (where one angle must be 90 degrees), as it would imply that all angles are 60 degrees.

2. Right isosceles: This type is possible. A right isosceles triangle has one angle of 90 degrees and the other two angles are each 45 degrees, with two sides of equal length.

3. Equilateral scalene: This is impossible because an equilateral triangle, by definition, has all three sides equal. A scalene triangle has all sides of different lengths.

4. Obtuse equilateral: This is also impossible because an equilateral triangle cannot have an angle greater than 60 degrees.

Thus, the only possible type of triangle based on the Triangle Inequality Theorem from the options provided is:

Right isosceles.