Question

triangle congruence: asa and aas
given: ( overline{ae} cong overline{dc} ), ( overline{ae} parallel overline{dc} )
prove: ( \triangle abe cong \triangle dbc )
complete the statements in the two - column proof.
enter your answers in the boxes.

statements	reasons
2. ( angle 1 cong angle square )	2. alternate interior angles theorem
3. ( angle square cong angle square )	3. vertical angles theorem
4. ( \triangle abe cong \triangle dbc )	4. aas

Explanation:

Step1: Analyze ∠1 ≅ ∠?

Since \( AE \parallel DC \), by alternate interior angles theorem, \( \angle 1 \) and \( \angle 5 \) are alternate interior angles. So \( \angle 1 \cong \angle 5 \).

Step2: Analyze ∠? ≅ ∠? (vertical angles)

Vertical angles are equal. \( \angle 2 \) and \( \angle 4 \) are vertical angles, so \( \angle 2 \cong \angle 4 \).

Answer:

1. \( \angle 1 \cong \angle 5 \)
2. \( \angle 2 \cong \angle 4 \)