Question

given: \\( \overline { a e } \cong \overline { d c } , \overline { a e } \parallel \overline { d c } \\)
prove: \\( \triangle a b e \cong \triangle d b c \\)
complete the statements in the two - column proof.
enter your answers in the boxes.

Explanation:

Step1: Alternate interior angles

Since \( \overline{AE}\parallel\overline{DC}\), by the alternate - interior angles theorem, \( \angle1\) and \( \angle5\) are alternate interior angles. So \( \angle1\cong\angle5\).

Step2: Vertical angles

By the vertical angles theorem, \( \angle2\) and \( \angle4\) are vertical angles. So \( \angle2\cong\angle4\).

Answer:

1. \(5\)
2. \(2\), \(4\)