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. ?

Answer 1

Answer:

A. is the answer

Step-by-step explanation:

Answer 2

Refer to the image attached.

Given: AB ∥ DE

To Prove: $\Delta ABC \sim \Delta EDC$

Statements                                                                                            

1. AB ∥ DE                                                                                                    

Reason: Given

2.$\angle$ACB and $\angle$ECD are vertical angles.

Reason: Definition of vertical angles

3. $\angle ACB \cong \angle DCE$

Reason: vertical angles are congruent

4. $\angle BDE and \angle DBA$ are alternate interior angles.

Reason: Definition of alternate interior angles

5. $\angle BDE \cong \angle DBA$

Reason: Alternate interior angles are congruent

6. $\Delta ABC \sim \Delta EDC$

Reason: By AA criteria

AA criteria for similarity states that "If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar".

Therefore, $\Delta ABC \sim \Delta EDC$