Question

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 = x
segment AD = y
y + x = c
c over a equals a over y and c over b equals b over x
a

Answer 1

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 = x
segment 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


Which is not a justification for the proof?
Pieces of Right Triangles Similarity Theorem
Side-Side-Side Similarity Theorem
Substitution
Addition Property of Equality