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 = y segment AD = x 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? Addition Property of Equality Pythagorean Theorem Pieces of Right Triangles Similarity Theorem Cross Product Property

Answer: Pythagorean Theorem Pieces of Right Triangles is not a justification for the proof.Explanation : Here, [tex]\triangle ABC[/tex] is a right triangle with sides a, b and c. Perpendicular CD forms right triangles BDC and CDA. CD measures h units, BD measures y units, DA measures x units.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 = y, segment AD = x,y + x = c a/c=y/a( Similarity theorem in triangles ABC and DBC )[tex]a^2 = cy[/tex]------(1) (Cross Product Property)Similarly, [tex]b^2 = cx[/tex] (Similarity theorem in triangles ABC and ADC)---------(2)[tex]a^2 + b^2 = cy + cx[/tex](after adding equation (1) and (2) )[tex]a^2 + b^2 = c(y + x)[/tex]( By additional property of equality)[tex]a^2 + b^2 = c^2[/tex]. ( because y + x=c)Thus, it has been proved that except Pythagorean Theorem Pieces of Right Triangles we use all other properties.