Which triangles are congruent by asa?

ΔABE ≅ ΔDEA

Step-by-step explanation:

From the given picture, In Δ ACE we have AC= CE

Then, ∠A=∠E     (1)  [∵Angles opposite to equal angles of a triangle are equal.]      

Also, it is given that ∠B=∠D=90°    [Right angle]

Now, Consider ΔABE and ΔDEA

Here,

∠A=∠E      [From (1)]

AE=AE         [By Reflexive property]

∠B=∠D=90°   [given]

Then, by ASA congruence postulate , ΔABE ≅ ΔDEA

ASA postulate says that if two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of other triangle, then the triangles are congruent.

Yes, two vertical lines can be complementary

Hope i can you!