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”) :}##

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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”) :}##

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