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.
