Question

proof #1: given: ∠a≅∠d prove: (overline{bc}congoverline{ef}) ∠c≅∠f (overline{ac}congoverline{df}) statements: ∠a≅∠d given ∠c≅∠f given (overline{ac}congoverline{df}) given (overline{bc}congoverline{ef}) cpctc

Explanation:

Step1: Recall triangle - congruence criteria

We have two angles and the included side of one triangle congruent to two angles and the included side of another triangle ($\angle A\cong\angle D$, $\overline{AC}\cong\overline{DF}$, $\angle C\cong\angle F$). By the ASA (Angle - Side - Angle) congruence criterion, $\triangle ABC\cong\triangle DEF$.

Step2: Use CPCTC

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. Since $\triangle ABC\cong\triangle DEF$, the corresponding sides $\overline{BC}$ and $\overline{EF}$ are congruent.

Answer:

The missing statements and reasons to complete the proof are:

Statements	Reasons
$\overline{BC}\cong\overline{EF}$	CPCTC