Questions: Given: CD bisects AE, AB CD angle E congruent to angle BCA Prove: triangle ABC congruent to triangle CDE

Write a paragraph proof.

Given: \(\overline{C D}\) bisects \(\overline{A E}\), \(\overline{A B} \parallel \overline{C D}\) \(\angle E \cong \angle B C A\)

Prove: \(\triangle A B C \cong \triangle C D E\)

Step Subtitle

We are given that \(\overline{C D}\) bisects \(\overline{A E}\). This means that \(\overline{A C} \cong \overline{C E}\). We are also given that \(\overline{A B} \parallel \overline{C D}\). Because of this, \(\angle B A C \cong \angle D C E\) since they are alternate interior angles. Finally, we are given that \(\angle E \cong \angle B C A\). Therefore, by Angle-Side-Angle (ASA) Congruence, we can conclude that \(\triangle A B C \cong \triangle C D E\).

\(\triangle ABC \cong \triangle CDE\) by ASA.

\(\triangle ABC \cong \triangle CDE\) by ASA.