Key properties: (1) If a:b = c:d, then (a+b):(a-b) = (c+d):(c-d); (2) Alternando: If a:b = c:d, then a:c = b:d; (3) Invertendo: If a:b = c:d, then b:a = d:c; (4) Componendo: If a:b = c:d, then (a+b):b = (c+d):d; (5) Dividendo: If a:b = c:d, then (a-b):b = (c-d):d; (6) Componendo-Dividendo: (a+b):(a-b) = (c+d):(c-d). Solving: Apply property matching the given condition. Example: From 5:7 = x:21, use inverse to find relationships. Shortcut: Memorize all six properties to spot MCQ patterns immediately. Exam tip: Property questions test conceptual clarity. Focus on when to apply which property based on given-find relationship.