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?
February 20th, 2023
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”)
:}##