B. Side-Side-Side Similarity Theorem is not justification for the proof. Properties & theorems used in the proof the Pythagorean Theorem:
Angle-Angle Similarity Theorem; Distributive Property; Addition Property of Equality; Substitution Property; Cross Product Property of Proportions; and Pieces of Right Triangle Similarity Theorem
However, you can't use the Pythagorean Theorem to prove itself.
The correct option is B. Side-Side-Side Similarity Theorem.
Given ΔABC is a right triangle.
To Prove: [tex]a^2 + b^2 = c^2[/tex]
The Justification given in question is below,
Draw an altitude from point C to Line segment AB
Let segment [tex]BC = a[/tex], segment [tex]CA = b[/tex] , segment [tex]AB = c[/tex] , segment[tex]CD = h[/tex]
segment [tex]DB = x[/tex] , segment [tex]AD = y[/tex]
c over a equals a over y and c over b equals b over x
[tex]a^2 = cy[/tex]; [tex]b^2 = cx[/tex]
Adding the above equations, [tex]a^2 + b^2 = cy + cx[/tex]
[tex]a^2+b^2=c(x+y)[/tex]
[tex]a^2 + b^2 = c(c)[/tex]
[tex]a^2 + b^2 = c^2[/tex]
From the justification giving in question, we found that it uses all the property except Side-Side-Side Similarity Theorem.
It uses Pieces of Right Triangles Similarity Theorem, Substitution, Addition Property of Equality etc.
Hence The correct option is B. Side-Side-Side Similarity Theorem.
For more details on proof of Pythagoras theorem follow the link below:
https://brainly.com/question/343682
