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.
To evaluate which of the given combinations of triangle types is possible, let's consider them one by one:
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Right Equilateral Triangle: An equilateral triangle has all sides equal and all angles equal to 60°. Since the angles cannot sum up to 90° in a right triangle (having one angle as 90°), a right equilateral triangle is not possible.
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Equilateral Scalene Triangle: An equilateral triangle cannot be scalene because an equilateral triangle has all sides of equal length. Thus, this combination is not possible.
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Right Isosceles Triangle: This type of triangle has two sides that are equal in length and includes a right angle (90°). This type is possible, and it adheres to the Triangle Inequality Theorem.
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Obtuse Equilateral Triangle: An equilateral triangle cannot have one angle greater than 90° because all angles are equal (60° each). Thus, this combination is not possible.
Given these evaluations, the only combination that is possible based on the Triangle Inequality Theorem is right isosceles.
1 answer