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
Right Isosceles Triangle
A right isosceles triangle cannot be constructed because the sum of the angles of a triangle must equal 180 degrees and with each angle being equal in an equilateral triangle each angle must equal 60 degrees. Therefore one cannot construct a 90 degree angle within this triangle.
Obtuse Equilateral Triangle
An obtuse equilateral triangle cannot be drawn because all angles in an equilateral triangle must be equal and must equal 60 degrees; therefore, it would not be possible to include an obtuse angle in that triangle.
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