Given: segment PS is congruent to segment QR; measure of angle PSR = measure of angle RQP = 90 Prove (using two-column proof): segment PQ is congruent to segment RS?

Use the and basic arithmetic axioms
as demonstrated below:

##{:
(color(black)(Assertion) | color(black)(Reason))
(bar(color(white)(XXXXXXXXXXXXXX))bar(color(white)(XXXXXXXXXXXX)))
(|PR|^2=|PS|^2+|SR|^2 | Pythagorean Theorem)
(|PR|^2=|QR|^2+|PQ|^2 | Pythagorean Theorem)
(|PS|^2+|SR|^2 = |QR|^2+|PQ|^2 | Equality Axiom)
(|PS|^2+|SR|^2 = |PS|^2 +|PQ|^2 | Given: |PS|=|PQ|)
(|SR|^2 = |PQ|^2 | Subtraction Axiom)
(|SR|=|PQ| | Positive Square Roots)
:}##