Question

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

statements	reasons
2. \\( \overline{b d} \cong \overline{b d} \\)	2. reflexive property of \\( \cong \\)
3. \\( \triangle a b d \cong \triangle c b d \\)	3. asa postulate (steps 1, 2)
4. \\( \overline{a b} \cong \overline{c b} \\)	4.

Explanation:

Step1: Recall triangle congruence properties

If two triangles are congruent, their corresponding parts are congruent.

Step2: Analyze the given proof steps

We have shown \(\triangle ABD\cong\triangle CBD\) (by ASA - Angle - Side - Angle postulate).

Step3: Apply the Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Since \(\triangle ABD\cong\triangle CBD\), then \(\overline{AB}\) and \(\overline{CB}\) are corresponding parts.

Answer:

1. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)