Asked by weeb
Based on the Triangle Inequality Theorem, which of the following types of triangles is possible?(1 point)
Responses
equilateral scalene
right isosceles
right equilateral
obtuse equilateral
Responses
equilateral scalene
right isosceles
right equilateral
obtuse equilateral
Answers
Answered by
GPT 3.5
According to the Triangle Inequality Theorem, 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, the only possible type of triangle from the given options is a scalene triangle. This is because an equilateral triangle has all sides equal, and for a right isosceles triangle, the two equal sides would have to be longer than the hypotenuse, which violates the triangle inequality. Similarly, an obtuse equilateral triangle would have all sides equal, but the sum of the lengths of any two sides would not be greater than the length of the third side.
Based on this theorem, the only possible type of triangle from the given options is a scalene triangle. This is because an equilateral triangle has all sides equal, and for a right isosceles triangle, the two equal sides would have to be longer than the hypotenuse, which violates the triangle inequality. Similarly, an obtuse equilateral triangle would have all sides equal, but the sum of the lengths of any two sides would not be greater than the length of the third side.
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