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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 with missing justifications proves the pythagorean theorem using similar triangles: statement justification draw an altitude from point c to line segment ab let segment bc = a segment ca = b segment ab = c segment cd = h segment db = x segment ad = y y + x = c c over a equals a over y and c over b equals b over x a2 = cy; b2 = cx a2 + b2 = cy + b2 a2 + b2 = cy + cx a2 + b2 = c(y + x) a2 + b2 = c(c) a2 + b2 = c2 which is not a justification for the proof? substitution addition property of equality transitive property of equality distributive property of equality