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, B

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? (5 points)

Substitution
Addition Property of Equality
Transitive Property of Equality
Distributive Property of Equality