Question

hl proof #2 given: $overline{pr}perpoverline{sq}$, $overline{pq}=overline{ps}$ prove: $\triangle prq=\triangle prs$ statements reasons

Explanation:

Step1: Identify right angles

∠PRQ = ∠PRS = 90° (PR ⊥ SQ, def of perpendicular)

Step2: Recognize right triangles

ΔPRQ and ΔPRS are right triangles (right angles at R)

Step3: Hypotenuse congruence

PQ ≅ PS (Given)

Step4: Common leg congruence

PR ≅ PR (Reflexive property)

Step5: Apply HL theorem

ΔPRQ ≅ ΔPRS (HL Congruence: hypotenuse & leg congruent)

Answer:

ΔPRQ ≅ ΔPRS