Write a paragraph proof.
Given: modifying above B C with bar congruent to modifying above E C with bar and Modifying above upper A upper C with bar congruent to Modifying above upper D upper C with bar
Prove: modifying above upper B upper A with barcongruent to Modifying above Upper E Upper D with bar
Segment B A is shown on the left. Segment D E is shown on the right. Segment B E intersects Segment A D at point C.
(5 points)
Given: $\overleftrightarrow{BC} \cong \overleftrightarrow{EC}$ and $\overline{AC} \cong \overline{DC}$
To prove: $\overline{BA} \cong \overline{ED}$
Proof:
1. $\overleftrightarrow{BC} \cong \overleftrightarrow{EC}$ (Given)
2. $\overline{AC} \cong \overline{DC}$ (Given)
3. $\overline{BC} \cong \overline{EC}$ (Definition of congruence)
4. $\angle BCA \cong \angle ECD$ (Vertically opposite angles are congruent)
5. $\triangle BCA \cong \triangle ECD$ (Side-Angle-Side congruence)
6. $\overline{BA} \cong \overline{ED}$ (Corresponding parts of congruent triangles are congruent)
Therefore, we have proved that $\overline{BA} \cong \overline{ED}$.