(9)
Given: \( \overline{A B} \cong \overline{C B} \)
\[
\overline{A D} \cong \overline{C E}
\]
Prove: \( \overline{D B} \cong \overline{E B} \)

Answer

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Answer

3. Since \( AB \cong CB \) and \( AD \cong CE \), \( DB \cong EB \)

Steps

Step 1 ：1. Given: \( \overline{A B} \cong \overline{C B} \) and \( \overline{A D} \cong \overline{C E} \)

Step 2 ：2. Apply subtraction to the given congruent segments: \( AB - AD = DB \), \( CB - CE = EB \)

Step 3 ：3. Since \( AB \cong CB \) and \( AD \cong CE \), \( DB \cong EB \)