Question

pr bisects ∠qrs and ∠qps. complete the proof that △prs ≅ △prq.
1 pr bisects ∠qrs given
2 pr bisects ∠qps given
3 ∠prq ≅ ∠prs definition of angle bisector
4 ∠qpr ≅ ∠rps definition of angle bisector
5 △prs≅△

Explanation:

Step1: Identify common side

$PR = PR$ (Reflexive Property of Congruence)

Step2: Apply ASA congruence

$\triangle PRS \cong \triangle PRQ$ (ASA: $\angle PRQ \cong \angle PRS$, $PR=PR$, $\angle QPR \cong \angle SPR$)

Answer:

$\triangle PRS \cong \triangle PRQ$ by ASA congruence criterion.