Question

sides of a triangle quick check
based on the triangle inequality theorem, which of the following types of triangles is possible?
(1 point)
○ right equilateral
○ equilateral scalene
○ obtuse equilateral
○ right isosceles

Explanation:

• A right equilateral triangle is impossible because in an equilateral triangle all angles are \(60^\circ\), not \(90^\circ\).
• An equilateral scalene triangle is impossible as equilateral (all sides equal) and scalene (all sides different) are contradictory.
• An obtuse equilateral triangle is impossible since all angles in an equilateral triangle are \(60^\circ\) (acute), not obtuse (\(> 90^\circ\)).
• A right isosceles triangle is possible (e.g., legs of length \(a\), hypotenuse \(a\sqrt{2}\), satisfying triangle inequality and having a right angle and two equal sides).

Answer:

D. right isosceles