This question can raise a lot of doubt. Thus, we will explore the activity in a pratical way, so that the explanation is clearer.

[justify]In the worksheet of "[url=https://www.geogebra.org/m/BTEXnCpe]Cases of Congruence[/url]"[url=https://ggbm.at/BTEXnCpe][/url] we can see that there are four cases: SAS (side-angle-side), ASA[br](angle-side-angle), SSS (Side-Side-Side[sub])[/sub] and AAS (angle-angle-side). It was natural to think that ASS (angle-side-side) or SSA (side-side-angle) would be possible. Why can't we use these situations as congruence[br]cases? In other words: Why is that two triangles, that have a congruent angle, an congruent adjacent side and an opposite congruent side, not necessarily be considered congruent?[/justify]

As the exercise already states, ALL cannot be considered a case of congruence, so we must prove that this is true. In order to prove this, we can simply show a case in which two triangles have a congruent angle, an congruent adjacent side and an opposite congruent side, and are not congruent.

Move points A, B or C and see if the triangles remain congruent. The question is, Would it be possible to build another triangle whose sides are congruent to AC and CB and that also have a congruent angle. Note that this new triangle is not congruent to ΔABC.