Question

complete the proof.
given :
\\( \frac { \angle b \cong \angle d } { \overline { a c } \cong \overline { e c } } \\)
prove: \\( \overline { a b } \cong \overline { e d } \\)

Explanation:

Step1: Vertical angles are congruent

$\angle ACB\cong\angle ECD$ (Vertical angles theorem)

Step2: Prove triangles congruent

In $\triangle ABC$ and $\triangle EDC$, we have $\angle B\cong\angle D$, $\angle ACB\cong\angle ECD$, and $AC\cong EC$. By the AAS (Angle - Angle - Side) congruence criterion, $\triangle ABC\cong\triangle EDC$.

Step3: Corresponding parts of congruent triangles

Since $\triangle ABC\cong\triangle EDC$, then $AB\cong ED$ (Corresponding parts of congruent triangles are congruent)

Answer:

$\overline{AB}\cong\overline{ED}$ is proved as shown above.