# Why can't there be an axiom of congruency of triangles as A.S.S. similar to R.H.S.?

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I think that, if we consider 2 triangles, whose one angle, the side opposite to that angle and any other side are equal, then the two triangles are congruent. If I am wrong, can someone please construct 2 non-congruent triangles with these conditions?

I think that, if we consider 2 triangles, whose one angle, the side opposite to that angle and any other side are equal, then the two triangles are congruent. If I am wrong, can someone please construct 2 non-congruent triangles with these conditions?

##### 1 Answer

Jul 18, 2016

(details below)

#### Explanation:

If

By construction

In triangles

and

So we have an A.S.S. arrangement

but