Answer:
Right Isosceles
Step-by-step explanation:
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Based on this theorem, let's analyze the given types of triangles:
- Obtuse Equilateral: An equilateral triangle has all sides of equal length. In an obtuse angle, one angle measures more than 90 degrees. For an equilateral triangle, all angles are 60 degrees (since the sum of all angles in a triangle is 180 degrees), so it cannot be obtuse.
- Right Isosceles: A right triangle has one angle of 90 degrees. An isosceles triangle has two sides of equal length. It's possible to have a right isosceles triangle where one angle is 90 degrees and the other two angles are 45 degrees each.
- Equilateral Scalene: An equilateral triangle has all sides of equal length, and a scalene triangle has all sides of different lengths. These two properties contradict each other, making an equilateral scalene triangle impossible.
- Right Equilateral: An equilateral triangle has all sides of equal length. It's not possible for an equilateral triangle to have a right angle (90 degrees) since the sum of angles in an equilateral triangle is 180 degrees.