Read the proof.

Given: AB ∥ DE

Prove: △ABC ~ △EDC

Triangles A B C and E D C connect at point C. Sides A B and D E are parallel.
Statement Reason
1. AB ∥ DE 1. given
2. ∠ACB and ∠ECD are vert. ∠s 2. definition of vertical angles
3. ∠ACB ≅ ∠DCE 3. vertical angles are congruent
4. ∠BDE and ∠DBA are alt. int. ∠s 4. definition of alternate interior angles
5. ∠BDE ≅ ∠DBA 5. alternate interior angles are congruent
6. △ABC ~ △EDC 6. ?
AA similarity theorem
ASA similarity theorem
AAS similarity theorem
SAS similarity theorem

Answer:

Its AA similarity theorem

Step-by-step explanation:

correct on edge 2021

The triangles ABC and EDC are similar by AA similarity theorem.

Two triangles are said to be similar if their corresponding sides are in equal ratio and corresponding angles are congruent.

Given is a proof of showing △ ABC ~ △ EDC

The proof is as follows :-

           Statement                                                Reason

            AB ∥ DE                                                     Given

         ∠ ACB = ∠ ECD                           definition of vertical angles  

         ∠ BDE ≅ ∠ DBA                   alternate interior angles are congruent

         △ ABC ~ △ EDC                                 AA similarity theorem

AA similarity theorem :-

AA similarity theorem states that when two corresponding angles of two triangles are found congruent then the triangles are similar by AA similarity theorem.

Hence, the missing reason is AA similarity theorem.

For more references on AA similarity theorem, click;

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