Question

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

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?

Answer 1

(details below)

Explanation:

If `C` is the center of a circle, the `abs(CB)=abs(CD)`

By construction
`color(white)("XXX")/_BAC=/_DAC`

In triangles `triangle BAC` and `triangle DAC`
`color(white)("XXX")/_BAC=/_DAC`
`color(white)("XXX")abs(AC)=abs(AC)`
and
`color(white)("XXX")abs(CB)=abs(CD)`

So we have an A.S.S. arrangement
but
`color(white)("XXX")triangle ACB` is not congruent to `triangle ACD`