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 = 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?

Pieces of Right Triangles Similarity Theorem

Side-Side-Side Similarity Theorem

Substitution

Addition Property of Equality