Question

Read the proof. Given: AB ∥ DE Prove: △ABC ~ △EDC 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 1

Answer:

AA similarity theorem

Step-by-step explanation:

When two triangles have two angles congruent then the two triangles are similar by AA similarity

Here we are given that AB is parallel to DE

AE and BD are joined to intersect at C.

Angle ACB = Angle ECD (vertically opposite angles_

Angle BDE = Angle DBA (alternate interior angles)

Hence the two triangles are similar by AA similarity theorem

Answer 2

the correct answer is  AA similarity theorem