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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?
Addition Property of Equality
Pythagorean Theorem
Pieces of Right Triangles Similarity Theorem
Cross Product Property

If you will look very closely at the operations and methods that were used to solve this problem, you will find that the Addition Property of Equality, the Pythagorean Theorem, and the Cross Product Property were all used as proof to solve this problem. So that eliminates the answers A., B., and D. So the only method that was not used as proof is the Pieces of Right Triangles Similarity Theorem.

So our answer is Pieces of Right Triangles Similarity Theorem.

Feel free to give brainliest.

vaughnjustin649 vaughnjustin649 · Answer 2 · 2020-10-30T14:49:07+01:00

Answer:

The answer is the Pieces of Right Triangles Similarity Theorem.

Step-by-step explanation :

look very closely at the operations and methods that were used to solve this problem, you will find that the Addition Property of Equality, the Pythagorean Theorem, and the Cross Product Property were all used as proof to solve this problem. To eliminate the answers A., B., and D. So the only method that was not used a proof is the Pieces of Right Triangles Similarity Theorem.

So our answer is C Pieces of Right Triangles Similarity Theorem.