Triangle A:
It has two equal sides, so it is isosceles
It has a right angle, so it is a right triangle
We conclude that triangle A is right and isosceles.
Triangle B:
It has two equal sides, so this is an isosceles triangle.
Triangle C:
It has a right angle, but none of its sides are equal, so this is a right triangle.
Triangle D:
All of its sides are equal, so this is an equilateral triangle.
Triangle E:
Two of its sides are equal, so this is an isosceles triangle.