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Anika [276]
3 years ago
8

Read the proof. Given: AB ∥ DE Prove: △ABC ~ △EDC Statement Reason 1. AB ∥ DE 1. given 2. ∠ACB and ∠ECD are vert. ∠s 2. definiti

on 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. ?

Mathematics
2 answers:
GrogVix [38]3 years ago
7 0

Answer:

A. is the answer

Step-by-step explanation:


olga2289 [7]3 years ago
3 0

Refer to the image attached.

Given: AB ∥ DE

To Prove: \Delta ABC \sim \Delta EDC

Statements                                                                                            

1. AB ∥ DE                                                                                                    

Reason: Given

2.\angleACB and \angleECD 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

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