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How About this....
Make a vector triangle such that the length and directions of the sides give the
Initial KE(Kinetic Energy) 1st object K=1/2 mv^2
Final KE of 1st object K1=1/2 mv1^2
Final KE of 2nd object K2=1/2 mv2^2
By Law of conservation kinetic energy for elastic collision
K=K1+K2 ==> v2= v1^2 + v2^2 ==> By Pythagoras Th. Angle between v1 and v2 should be 90 degrees.
I think this works <==> angle not equal to 0 and 90 given that the second object is initially at rest and both are of same mass.
you could prove this too by taking final resultant momenta of the initial momentum and do lil'bit of trig... and this one would be it's special case......... but just to prove the final momenta are at right angles this should be enough.....
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