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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. ?

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gungamer720

Answer:

A. is the answer

Step-by-step explanation:


MrRoyal

Similar triangle may or may not be congruent.

The statement that completes the proof of [tex]\mathbf{\triangle ABC \sim \triangle EDC}[/tex] is similar by ASA

From the question, we have the following highlights.

  • [tex]\mathbf{\angle ACB \cong \angle DCE}[/tex].
  • [tex]\mathbf{\angle DBA \cong \angle BDE}[/tex].
  • [tex]\mathbf{AB \parallel DE}[/tex].

The above highlights mean that:

  • Two corresponding angles of both triangles are congruent (this represents AA)
  • One corresponding side of both triangles is congruent (this implies ASA).

Hence, [tex]\mathbf{\triangle ABC \sim \triangle EDC}[/tex] is similar by ASA

Read more about proofs of similar triangles at:

https://brainly.com/question/4735192

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