Right triangle ABC is isosceles and point M is the midpoint of the hypotenuse.

Right triangle A B C is shown. Point M is the midpoint of the hypotenuse. The lengths of sides A B and B C are congruent. The lengths of line segments A M and M C are congruent.

What is true about triangle AMB?

It is congruent to triangle ABC.
It is an obtuse triangle.
It is an isosceles right triangle.
It is a scalene triangle.