Question

Based on the Triangle Inequality Theorem, which of the following types of triangles is possible?(1 point)%0D%0AResponses%0D%0A%0D%0Aobtuse equilateral%0D%0Aobtuse equilateral%0D%0A%0D%0Aright equilateral%0D%0Aright equilateral%0D%0A%0D%0Aright isosceles%0D%0Aright isosceles%0D%0A%0D%0Aequilateral scalene

Answer 1

To determine which types of triangles are possible based on the Triangle Inequality Theorem, we can analyze the options given:

1. **Obtuse Equilateral**: This is not possible. An equilateral triangle has all angles equal to 60 degrees, which is not obtuse.

2. **Right Equilateral**: This is also not possible. A right triangle has one angle of 90 degrees, while in an equilateral triangle all angles measure 60 degrees.

3. **Right Isosceles**: This is possible. A right isosceles triangle has one 90-degree angle and two 45-degree angles, fitting within the principles of the Triangle Inequality Theorem.

4. **Equilateral Scalene**: This is not possible. An equilateral triangle has all sides equal, while a scalene triangle has no equal sides.

Therefore, the type of triangle that is possible from the options provided is **right isosceles**.