Prove that right triangles are equal in hypotenuse and acute angle.

Given:
right-angled triangle ABC,
right-angled triangle A1B1C1,
angle A and angle A1 – right angles,
ВС = В1С1,
angle C = angle C1.
Prove that triangle ABC = A1B1C1.
Decision:
Consider triangles ABC and A1B1C1. We know that the sum of the degree measures of any triangle is 180 degrees. Since angle A = angle A1 = 90 degrees and angle C = angle C1, then angle B = angle B1. By the condition of the hypotenuse BC = B1C1. Therefore, along the side and two adjacent corners, the triangle ABC = triangle A1B1C. Q.E.D.