An obtuse triangle has one angle that is greater than 90^(∘).
Right isosceles triangle?: Yes. Right equilateral triangle?: No.
Practice makes perfect
Right isosceles triangle
A right triangle is a triangle where one angle is 90^(∘). Let's start with drawing a right angle.
The next requirement is that the triangle is isosceles which means two of the triangles sides have to be congruent. By extending the legs that make up the 120^(∘) angle with the same length, and then connecting the endpoints, we have created an isosceles right triangle.
Note that this was just one example. There is an infinite number of triangles we could have created.
Right equilateral triangle
An equilateral triangle has three congruent sides which makes all three angles congruent as well. This means each angle will have a measure of 60^(∘).
180^(∘)/3=60^(∘).
Therefore, a right equilateral triangle does not exist.
