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?
A. Substitution
B. Addition Property of Equality
C. Transitive Property of Equality
D. Distributive Property of Equality

Answer:There is a misprint in the question.In the statement you have written DB=x ,and DA=y but in Question you have written DA= x and DB=y.So, let me just considering your Statement justificationLet segment BC = a, segment CA = b ,segment AB = c segment CD = h, segment DB = x, segment AD = y ,y + x = cIn Δ B DC and Δ BC A∠B D C =∠B C A [each being 90°]∠ B is common.Δ B D C is similar to Δ BC A.⇒ a² = c x .........(1)Similarly we can prove that Δ ADC is similar to Δ BC A.⇒b²= c y ......(2)adding (1) and (2)⇒ =c×c [∴ x+y =c] =c²So, we have used two properties 1. Right Triangles Similarity Theorem 2.Substitution Addition Property of Equality.we haven't used Side-Side-Side Similarity Theorem. It is not the right justification for the proof.

Step-by-step explanation: