question_answer

Which of the following criterion does not exist in the field of congruency of triangles.

A)  A.S.A. criterion          

B)  R.H.S. criterion

C)  A.A.A. criterion   

D)  S.S.S. criterion

Correct Answer: C

Solution :

(c): AAA criterion means corresponding \[\angle les\] are equal. But this is easily seen to fail us. For e.g.                         \[\angle x=\angle {{x}_{1}}\] \[\angle y=\angle {{y}_{1}}\]; Hence, although shapes are same, sizes are different. \[\angle z=\angle {{z}_{1}}\] Mind of a mathematician: In mathematics, if you can find even one example contrary to the given proposition, then the proposition is wrong. By the above example, we can see that AAA does not hold for congruency.