Can you draw an equilateral right triangle? Explain using precise mathematical language.

No.

Step-by-step explanation:

An equilateral triangle is made when all three sides of the triangle are congruent, which means that the angles will also be congruent. A right triangle is defined by its 90° angle. The total angle measures of a triangle add up to 180°. This means that the other two angles have to add up 90° because one measure is already half of 180. Since the measures have to add up to 90, they won't each be equal to 90. This means that the triangle won't be equilateral. (or, you can't have three 90° angles in a triangle because that would pass the 180° measure)

Also, the use of the Pythagorean theorem shows that the sum of the legs squared is equal to the hypotenuse. Thus, the hypotenuse in a right triangle will always be the longest side, which means that it can't be an equilateral triangle.