Question

Given: ∆BCA 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 two-column proof with missing justifications proves the Pythagorean Theorem using similar triangles.

Answer 1

chart

Statement

Justification
Draw an altitude from point C to Line Segment AB


Let Line Segment BC= a
Line Segment CA= b
Line Segment AB= c
Line Segment CD= h
Line Segment DB= x
Line Segment AD= y


y + x = c


c over a is equal to a over y; c over b is equal to 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

Answer 2

Which is NOT a justification for the proof?

Substitution

Addition Property of Equality

Transitive Property of Equality

Distributive Property of Equality

Answer 3

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