Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
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.
Feel free to ask if you would like to delve deeper into any specific part!