Question

fill in the missing statement and reason of the proof below.
given: ∠dae ≅ ∠dbe and overline{ac} ≅ overline{bc}.
prove: overline{dc} bisects ∠acb.
step statement reason
1 ∠dae ≅ ∠dbe overline{ac} ≅ overline{bc} given
2 overline{ad} ≅ overline{bd} in a triangle, sides opposite of congruent angles are congruent
3 overline{cd} ≅ overline{cd} reflexive property
4 △acd ≅ △bcd sss
5 ∠acd ≅ ∠bcd select a reason
6 overline{dc} bisects ∠acb a segment that divides a larger angle into two congruent angles bisects that larger angle
note: overline{ce} and overline{ab} are segments

Explanation:

Step1: Recall the property of congruent triangles

When two triangles are congruent (in this case, $\triangle ACD\cong\triangle BCD$ by SSS - Side - Side - Side congruence criterion as $\overline{AC}\cong\overline{BC}$, $\overline{AD}\cong\overline{BD}$, $\overline{CD}\cong\overline{CD}$), their corresponding parts are congruent.

Step2: Identify the corresponding angles

The corresponding angles of $\triangle ACD$ and $\triangle BCD$ are $\angle ACD$ and $\angle BCD$.

Answer:

The missing statement is $\angle ACD\cong\angle BCD$ and the reason is "Corresponding parts of congruent triangles are congruent (CPCTC)".