Why there is no Angle Side Side - Maths - Congruence of Triangles

Question

Why there is no Angle Side Side

Harleen Birdi · Accepted Answer

Let us consider two triangles ABC and PQS.

In ΔPQS, we have PQ = PR

We have AB = PQ (= PR),

AC = PS

and ∠ACB = ∠PSQ (= ∠PSR)

If angle -side-side congruency exists, then ΔABC $≅$ ΔPQS.

But by same congruency criterion, we have ΔABC $≅$ ΔPRS.

or we can say that ΔPRS $≅$ ΔPQS, which is not possible (as ΔPRS is a part of ΔPQS)

Therefore, such a congruency does not exist.