Question

based on the given diagram, complete the flowchart proof below.
∠bac ≅ ∠dca
reason:
given
(overline{ab} cong overline{dc})
reason:
select reason
(overline{ac} cong overline{ac})
reason:
reflexive property
(\triangle abc cong \triangle cda)
reason:
select reason

Explanation:

Step1: Identify segment congruence reason

The diagram shows tick marks on $\overline{AB}$ and $\overline{DC}$, which indicates they are congruent by the given diagram markings.

Step2: Identify triangle congruence reason

We have $\angle BAC \cong \angle DCA$ (given), $\overline{AB} \cong \overline{DC}$ (from diagram), and $\overline{AC} \cong \overline{AC}$ (reflexive property). This matches the Side-Angle-Side (SAS) congruence criterion.

Answer:

1. For $\overline{AB} \cong \overline{DC}$, Reason: Given (from diagram markings)
2. For $\triangle ABC \cong \triangle CDA$, Reason: Side-Angle-Side (SAS) Congruence Postulate