Question

Sides of a Triangle Quick Check 3 of 53 of 5 Items Question Based on the Triangle Inequality Theorem, which of the following types of triangles is possible?(1 point) Responses obtuse equilateral obtuse equilateral equilateral scalene equilateral scalene right equilateral right equilateral right isosceles right isosceles Skip to navigation page 15 of 15

Answer 1

Based on the Triangle Inequality Theorem, a triangle can be any type of triangle as long as the lengths of the sides adhere to the principle that the sum of the lengths of any two sides must be greater than the length of the third side.

Given the options you provided, at least one of the triangle types is possible. Here's a quick overview:

1. Equilateral: All sides are equal, satisfying the triangle inequality.
2. Scalene: All sides are different lengths, which can also satisfy the triangle inequality.
3. Isosceles: Two sides are equal, thus satisfying the triangle inequality.
4. Right: One angle is 90 degrees, which can be achieved with appropriate side lengths.
5. Obtuse: One angle is greater than 90 degrees, which can also be achieved with appropriate side lengths.

Since you asked specifically about types of triangles based on the given responses, all options mentioned (equilateral, scalene, right, and isosceles) can be valid triangles as long as the respective side lengths satisfy the triangle inequality theorem.

If you have a specific set of side lengths in mind or if you need help with a specific choice, please clarify!