In Triangle Abc, ∠A = 30°, ∠B = 40° and ∠C = 110° in Triangle Pqr, ∠P = 30°, ∠Q = 40° and ∠R = 110° a Student Says that Triangle Abc ≅ Triangle Pqr by Aaa Congruence Criterion. is He Justified? Why Or Why Not? - Mathematics
In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°
In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°
A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?
No. This property represents that these triangles have their respective angles of equal measure. However, this gives no information about their sides. The sides of these triangles have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two triangles congruent.