Given that in two right angle triangles one side and acute angle of one are equal to the corresponding side and angle of the other.

We have to prove that the triangles are congruent.

Let us consider two right angle triangles. Such that,

∠B = ∠E = 90^o (i)

AB = DE (ii)

∠C = ∠F (iii)

Now, observe the two triangles ABC and DEF

∠C = ∠F (iv)

∠B = ∠E [From (i)]

AB = DE [From (ii)]

So, by AAS theorem, we have

Hence, proved