Why does the ASS (or SSA) can't be used to determine triangle congruence?
- Jorge Cássio
Why is not the ALL or LLA a case of congruence between triangles?
In the worksheet of "Cases of Congruence" we can see that there are four cases: SAS (side-angle-side), ASA (angle-side-angle), SSS (Side-Side-Side) 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 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?
Construction of a congruent triangle to ΔABC in which the only measures given are of two sides and of an angle.
Construção de dois triângulos que possuem ordenadamente congruentes um ângulo, o lado adjacente e o lado oposto e não são congruentes.
Would it be possible to find another triangle that had an angle, an adjacent side and an opposite side, all of them congruent, and that was not congruent to the triangle ABC?