Question

Given ∠ABE = 45° and ∠EAB = 63° in ΔABE and∠MNP= 72° and ∠NMP = 63° in ΔMNP. Are the two triangles, ΔABE and ΔMPN similar? If so, by what criterion? A) yes, by AA criterion B) yes, by SAS criterion C) yes, by SSA criterion D) no, not possible to tell.

Answer 1

∠AEB = 180 - ∠ABE - ∠EAB = 180 - 45 - 63 = 72°

∠EAB in ΔABE = ∠NMP in ΔMNP = 63°
and
∠AEB in ΔABE = ∠MNP in ΔMNP = 72°

Two triangles are similar if two corresponding angles are equal to each other, so the answer is A) yes, by AA criterion