Question

complete the proof that $\triangle pqr \cong \triangle prq$.

statement	reason
2. $\angle p \cong \angle p$
3. $\triangle pqr \cong \triangle prq$

Explanation:

Step1: Identify given congruent sides

$\overline{PR} \cong \overline{PQ}$ (Given, marked on diagram)

Step2: Identify common angle

$\angle P \cong \angle P$ (Reflexive Property of Congruence)

Step3: Identify unstated congruent side

$\overline{PQ} \cong \overline{PR}$ (Given, restated for clarity)

Step4: Apply SAS congruence rule

$\triangle PQR \cong \triangle PRQ$ (Side-Angle-Side (SAS) Congruence Postulate)

Answer:

1. Reason: Given
2. Reason: Reflexive Property of Congruence
3. Reason: Side-Angle-Side (SAS) Congruence Postulate