Prove ΔAED ≅ ΔBED by moving justifications into the table. Given: ∠AED ≅ ∠BED and ∠EAD ≅ ∠CBF Statement: ∠AED ≅ ∠BED and ∠EAD ≅ ∠CBF ∠CBF ≅ ∠DBE ∠EAD ≅ ∠DBE DE ≅ DE ΔAED ≅ ΔBED Justification: Given Vertical angles are congruent Reflexive Property Symmetric Property Angle – Angle – Side

To prove that triangles ΔAED and ΔBED are congruent, we’ll organize the statements and justifications clearly into a table format.

| Statement | Justification |

|————————————|—————————————–|

| ∠AED ≅ ∠BED and ∠EAD ≅ ∠CBF | Given |

| ∠CBF ≅ ∠DBE | Vertical angles are congruent. |

| ∠EAD ≅ ∠DBE | Symmetric Property |

| DE ≅ DE | Reflexive Property |

| ΔAED ≅ ΔBED | Angle-Angle-Side (AAS) Congruence |

### Explanation:

– Given angles are congruent as stated in the problem.

– Vertical angles are always congruent, so ∠CBF ≅ ∠DBE.

– By the symmetric property, we can state that if ∠EAD ≅ ∠CBF, then ∠EAD ≅ ∠DBE.

– The segment DE is congruent to itself by the reflexive property.

– Finally, we can conclude that the two triangles are congruent by the Angle-Angle-Side (AAS) congruence criterion since we have two pairs of angles and a non-included side congruence.

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