The sign of equality of right-angled triangles along the hypotenuse and leg.

If the hypotenuse and leg of one right triangle are respectively equal to the hypotenuse and leg of the other right triangle, then these triangles are equal.
Evidence
Let triangles ACB (angle C = 90 degrees) and ACE (angle C = 90 degrees) be given, AC = AC – legs, AB = AE – hypotenuses.
Let’s combine these triangles with equal legs, as shown in the figure. Since AB = AE, the resulting triangle BAE is isosceles, then AB and AE are the lateral sides, and BE is the base, angles ABE (aka acute angle ABC of a right-angled triangle ACB) and AEB (aka acute angle AEC of a right-angled triangle ACE) – angles at the base of an isosceles triangle. Since the angles at the base of an isosceles triangle are equal, then the angle ABE (angle ABC) = angle AEB (angle AEC).
Then two right-angled triangles ACB and ACE are equal in hypotenuse (AB = AE) and acute angle (ABC and AEC).