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 two-column proof with missing justifications proves the pythagorean theorem using similar triangles:

which is not a justification for the proof?

substitution

addition property of equality

transitive property of equality

distributive property of equality