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.
1. Obtuse equilateral triangle: This is not possible because an equilateral triangle has three equal sides and all angles are 60 degrees, which is less than 90 degrees. The sum of any two sides will always be greater than the third side, so it violates the Triangle Inequality Theorem.
2. Right isosceles triangle: This is possible. In a right isosceles triangle, two sides are equal in length and the third side (the hypotenuse) is longer. The sum of the two equal sides will always be greater than the length of the hypotenuse, so it satisfies the Triangle Inequality Theorem.
3. Equilateral triangle: This is possible. An equilateral triangle has three equal sides, so the sum of any two sides will always be greater than the length of the remaining side, satisfying the Triangle Inequality Theorem.
4. Scalene equilateral triangle: This is not possible because a scalene triangle has three sides of different lengths, and an equilateral triangle has three sides of equal length.
5. Right equilateral triangle: This is not possible because an equilateral triangle has three equal angles of 60 degrees, so it can't have a right angle of 90 degrees. The sum of the two equal sides will always be greater than the length of the remaining side, so it satisfies the Triangle Inequality Theorem.
Therefore, the possible types of triangles are:
- Right isosceles
- Equilateral
Based on the Triangle Inequality Theorem, which of the following types of triangles is possible?(1 point) Responses obtuse equilateral obtuse equilateral right isosceles right isosceles equilateral scalene equilateral scalene right equilateral
1 answer
1 answer