6. Given: $\overline{A B} \cong \overline{C B}, \overline{A D} \cong \overline{C D}$ Prove : $\angle B A D \cong \angle B C D$ Statement 1. $\overline{A B} \cong \overline{C B}, \overline{A D} \cong \overline{C D}$ 2. 3. 4. 1. Given 2. 3. 4.

Step 1 ：Given: \(\overline{AB} \cong \overline{CB}\), \(\overline{AD} \cong \overline{CD}\)

Step 2 ：Since \(\overline{AB} \cong \overline{CB}\) and \(\overline{AD} \cong \overline{CD}\), we can use the Side-Side-Side (SSS) congruence theorem to prove that \(\triangle ABD \cong \triangle CBD\)

Step 3 ：Therefore, \(\angle BAD \cong \angle BCD\)

Step 4 ：\(\boxed{\angle BAD \cong \angle BCD}\)