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Problem 87

Given: \(\angle A \cong \angle D, A E \cong D E, A C \cong \underline{D B} .\) Prove: \(\Delta A B E \cong \triangle D C E\).

Expert verified

Given: \(\angle A \cong \angle D\), \(A E \cong D E\), and \(A C \cong D B\).
Applying ASA Postulate since:
1. \(\angle A \cong \angle D\) - Angle
2. \(A E \cong D E\) - Side (included between the angles)
3. \(\angle A B E \cong \angle D C E\) - Angle (Vertical angles)
Hence, by ASA Congruence Postulate, \(\Delta A B E \cong \triangle D C E\).

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