Question

the proof that \\( \triangle a c b \cong \triangle e c d \\) is shown.
given: \\( \overline{a e} \\) and \\( \overline{d b} \\) bisect each other at c.
prove: \\( \triangle a c b \cong \triangle e c d \\)
what is the missing statement in the proof?
\\( \angle b a c \cong \angle d e c \\)
\\( \angle a c d \cong \angle e c b \\)
\\( \angle a c b \cong \angle e c d \\)
\\( \angle b c a \cong \angle d c a \\)

Explanation:

Step1: Vertical angles definition

Vertical angles are formed when two lines intersect. In this case, lines \(AE\) and \(DB\) intersect at \(C\).

Step2: Vertical angles property

Vertical angles are congruent. \(\angle ACB\) and \(\angle ECD\) are vertical angles.

Answer:

\(\angle ACB\cong\angle ECD\)