Question

In two right triangles, one side and acute angle of one triangle are equal to one side and the corresponding acute angle of the other triangle, prove that the two triangles are congruent.

Answer 1

LETS NAME BOTH THE TRIANGLES AS ABC & DEF.
IN TRIANGLE ABC & DEF:
BC=EF
ANGLE ACB=DFE
SINCE BOTH ARE RIGHT ANGLED TRIANGLE
ANGLE ABC=DEF

SO,TWO ANGLE AND ONE SIDE IS EQUAL.
BY ASA CONGRUENCE CONDITION BOTH THE TRIANGLES ARE EQUAL. 

I HOPE THIS HELPED.