Triangles can be classified by their side lengths (scalene, isosceles, and equilateral), and by their angle measure (acute, right, and obtuse). However, not all combinations of these classifications exist.

Do each of the following triangles exist? If yes, draw the triangle accurately, with measurements. If no, explain why it cannot exist.

  • a right isosceles triangle
  • a right equilateral triangle
  • a right scalene triangle
  • an acute scalene triangle
  • an acute isosceles triangle
  • an acute equilateral triangle
  • an obtuse scalene triangle
  • an obtuse isosceles triangle
  • an obtuse equilateral triangle