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 proves the Pythagorean Theorem using similar triangles.
Statement Justification
Draw an altitude from point C to Line segment AB By construction
Let segment BC = a
segment CA = b
segment AB = c
segment CD = h
segment DB = y
segment AD = x By labeling
y + x = c ?
c over a equals a over y and c over b equals b over x Pieces of Right Triangles Similarity Theorem
a2 = cy; b2 = cx Cross Product Property
a2 + b2 = cy + b2 Addition Property of Equality
a2 + b2 = cy + cx Substitution
a2 + b2 = c(y + x) Distributive Property of Equality
a2 + b2 = c(c) Substitution
a2 + b2 = c2 Multiplication
Which of the following is the missing justification in the proof?
Transitive Property of Equality
Segment Addition Postulate
Substitution
Addition Property of Equality
1 answer
1 answer