An isosceles right triangle.
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A scalene triangle has no equal sides and no right angle.
It is an isosceles right angle triangle that has two equal sides which has two 45 degree angles and a 90 degree angle.
The dimensions of any right angle triangle other than an isosceles right triangle which has two equal sides.
No, all three sides of a right angle triangle cannot be equal. In a right angled triangle, the side opposite the right angle - the hypotenuse - will always be the longest side of the triangle. The remaining two sides may be equal to each other, but they don't have to be.
A triangle with one right angle and two equal sides is called an isosceles right angled triangle.