Question

If ∠A ≅∠D and ∠C ≅∠F, which additional statement does NOT allow you to conclude that ΔABC ≅ ΔDEF

Answer 1

AC is congruent to DF doesn’t allow you to conclude the triangles are similar I believe

Answer 2

Answer:

The answer is $\angle B \simeq \angle E$

Step-by-step explanation:

to say when two triangles are congruent, there are some criteria. I put here one of them but there are others like SSS critera, SAS criteria that you can find in a text of geometry or in the internet.

The ASA criteria (Angle, Side, Angle) says that if two triangles have the same measure for two corresponding angles and the side between them, then the triangles are congruent.

So, first, note that by the triangle angle theorem you can conclude that if  ∠A ≅∠D and ∠C ≅∠F (only with those hypotesis)  we must have  ∠B ≅∠E.

With that in mind and the ASA criteria we have that any of the first three hypotesis allows us to conclude that the two triangles are congruent.

But the last hypotesis does not allows us to conclude it because we can have two triangles with all its corresponding angles congruent but one triangle bigger than the other one.