MATH SOLVE

2 months ago

Q:
# Which is not a justification for the proof? A. Pieces of Right Triangles Similarity Theorem B. Side-Side-Side Similarity Theorem C. Substitution D. Addition Property of EqualityGiven: ΔABC is a right triangle.Prove: a2 + b2 = c2The two-column proof with missing justifications proves the Pythagorean Theorem using similar triangles:StatementJustificationDraw an altitude from point C to Line segment AB Let segment BC = asegment CA = bsegment AB = csegment CD = hsegment DB = xsegment 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

Accepted Solution

A:

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 TheoremHowever, you can't use the Pythagorean Theorem to prove itself.