Question

fill in the missing statement and reason of the proof below.
given: \\( \angle d a e \cong \angle d b e \\) and \\( \overline{a c} \cong \overline{b c} \\).
prove: \\( \overline{d c} \\) bisects \\( \angle a c b \\).

Explanation:

Step1: Recall the property of congruent triangles

Since \(\triangle ACD\cong\triangle BCD\) (from step 4), corresponding parts of congruent triangles are congruent.

Step2: Identify the corresponding angles

\(\angle ACD\) and \(\angle BCD\) are corresponding angles of \(\triangle ACD\) and \(\triangle BCD\).
So, \(\angle ACD\cong\angle BCD\)

Answer:

Statement: \(\angle ACD\cong\angle BCD\); Reason: Corresponding parts of congruent triangles are congruent (CPCTC)