Question

given: $overline{ae}congoverline{dc}$, $overline{ae}paralleloverline{dc}$
prove: $\triangle abecong\triangle dbc$
complete the statements in the two - column proof.
enter your answers in the boxes.
statements reasons

1. $overline{ae}congoverline{dc}$, $overline{ae}paralleloverline{dc}$ 1. given
2. $angle1conganglesquare$ 2. alternate interior angles theorem
3. $anglesquareconganglesquare$ 3. vertical angles theorem
4. $\triangle abecong\triangle dbc$ 4. aas

Explanation:

Step1: Identify 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: Identify vertical angles

$\angle2$ and $\angle4$ are vertical angles. By the vertical angles theorem, $\angle2\cong\angle4$.

Answer:

1. $\angle5$
2. $\angle2$, $\angle4$