text: PS is the altitude means that PS is perpendicular to QR.\nSo <PSQ is a right angle.\nUse the pythagorean theorem.\n\n(QS)^2 + (PS)^2 = (PQ)^2\nand\n(RS)^2 + (PS)^2 = (PR)^2\nsubtract one from the other to get:\n\nEQUATION 1: (QS)^2 - (RS)^2 = (PQ)^2 - (PR)^2\nso if QS ≠ RS then (QS)^2  ≠ (RS)^2\nsubtract (RS)^2 from both sides to get:\n(QS)^2 - (RS)^2 ≠ 0\nsubstitute this into EQUATION 1 to get:\n0 ≠ (PQ)^2 - (PR)^2\nadd (PR)^2 to both sides:\n(PQ)^2 ≠ (PR)^2\nand since all values are positive, we can take the principle square root of both sides to get:\nPQ ≠ PR