Prove a point is on the angle bisector if and only if it is equally distant from the two sides of the angle.
Prove a point is on the angle bisector if and only if it is equally distant from the two sides of the angle.
You do understand that this is not a homework service?
So you need to show some effort.
Here are the operative theorems.
If one acute angle and a leg of one right triangle are congruent to one acute angle and a leg of another right triangle then the triangles are congruent.
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle then the triangles are congruent.