There are two triangles ABC and DEF with corresponding sides abc and def. Given that angle D = angle E, and angle A = angle C, and side b = side e, determine if the triangles are congruent.
The answer is yes based on the theorem that two angles and a side of one triangle is equal to two angles and a side of another triangle.
My question is it only gives that two angles are equal in each triangle, it never says angle A = angle D. How then can the triangles be congruent?
These triangles don't have to be congruent.
Let's take triangle with angles $A,C,B$ $30^\circ, 30^\circ, 120^\circ $ and side $b=1$, and another one with angles $D,E,F$ $45^\circ, 45^\circ, 90^\circ $ and side $e=1$. These fulfill the conditions given, but obviously are not congruent.