Final answer:
The missing justification in the proof is substitution. The proof uses similar triangles and the Pythagorean theorem to show that a2 + b2 = c2.
Step-by-step explanation:
The missing justification in the proof is substitution. Here is the step-by-step explanation of the proof:
- Draw an altitude from point C to line segment AB.
- Segment BC = a, Segment CA = b, Segment AB = c (given information).
- Segment CD = h, Segment DB = y, Segment AD = x (given information).
- Using similar triangles, we can write the following ratios: c/a = a/y and c/b = b/x.
- Cross-multiplying these ratios gives us a2 = cy and b2 = cx.
- Substituting these equations into the equation a2 + b2 = c2, we get c2 = cy + cx.
- Simplifying further, c2 = c(y + x).
- Finally, factoring out c from the right side gives us c2 = c(c).
- And simplifying one last time, we get c2 = c2.