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

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.

Out of the options you've provided, let's analyze each:

1. Right Equilateral: This is not possible, as an equilateral triangle has all sides equal and all angles equal to 60°, while a right triangle must have one angle equal to 90°.

2. Right Isosceles: This is possible. A right isosceles triangle has two sides of equal length and one right angle.

3. Right Isosceles: This is the same option as listed before and is still possible.

4. Obtuse Equilateral: This is not possible, as an equilateral triangle cannot have an angle greater than 60°.

5. Obtuse Equilateral: This repeats the previous option and is not possible.

6. Equilateral Scalene: This is not possible, as an equilateral triangle cannot be scalene by definition (equilateral means all sides are equal).

So, the only possible type of triangle from the options provided is Right Isosceles.