Given: ΔABC is a right triangle.
Prove: a2 + b2 = c2
Right triangle BCA with sides of l...
Mathematics, 12.12.2020 16:10 maddigrace3
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
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