Given: ΔABC is a right triangle. Prove: a2 + b2 = c2 Right triangle BCA with sides of length a, b, and c. Perpendicular CD forms right triangles BDC and CDA. CD measures h units, BD measures y units, DA measures x units. The following two-column proof proves the Pythagorean Theorem using similar triangles. Statement Justification Draw an altitude from point C to Line segment AB By construction Let segment BC = a segment CA = b segment AB = c segment CD = h segment DB = y segment AD = x By labeling y + x = c ? c over a equals a over y and c over b equals b over x Pieces of Right Triangles Similarity Theorem a2 = cy; b2 = cx Cross Product Property a2 + b2 = cy + b2 Addition Property of Equality a2 + b2 = cy + cx Substitution a2 + b2 = c(y + x) Distributive Property of Equality a2 + b2 = c(c) Substitution a2 + b2 = c2 Multiplication Which of the following is the missing justification in the proof? Transitive Property of Equality Segment Addition Postulate Substitution Addition Property of Equality