Which of these triangles do not eist?

a scalene right triangle
an isosceles right triange
an eguilateral right triangle
an equilateral acute triangle

An equilateral triangle has all the angles equal, and each is 60°.

Now please reread the list and see if you can find the answer!

To determine which of these triangles do not exist, we need to evaluate the properties of each type of triangle.

1. Scalene Right Triangle: A scalene triangle is one in which all three sides have different lengths. A right triangle has one angle that measures 90 degrees. Therefore, a scalene right triangle must have all sides of different lengths and one 90-degree angle. This triangle is possible and does exist.

2. Isosceles Right Triangle: An isosceles triangle has two sides of equal length. In a right triangle, one angle measures 90 degrees. If we have an isosceles right triangle, it means that the two equal sides form the right angle. Since equilateral triangles are the only type of triangle with three equal sides, an isosceles right triangle is not possible and does not exist.

3. Equilateral Right Triangle: An equilateral triangle has three equal sides. In a right triangle, one angle measures 90 degrees. If we have an equilateral right triangle, it means that each angle must measure 60 degrees (180 divided by 3) since all angles in an equilateral triangle are equal. However, the sum of the angles in a triangle is always 180 degrees, so it is not possible to have a 90-degree angle and three 60-degree angles in the same triangle. Therefore, an equilateral right triangle does not exist.

4. Equilateral Acute Triangle: An equilateral triangle has three equal sides. An acute triangle is a triangle where all three angles are less than 90 degrees. Since all angles in an equilateral triangle measure 60 degrees, an equilateral triangle cannot be acute. Therefore, an equilateral acute triangle does not exist.

In summary, the isosceles right triangle and the equilateral acute triangle do not exist.