Question

statement justification draw an altitude from point c to ab by construction let bc = a ca = b ab = c cd = h db = y ad = x by labeling y + x = c? c/a = a/y, c/b = b/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

Explanation:

The Segment Addition Postulate states that if we have a line - segment $\overline{AB}$ and a point $D$ on $\overline{AB}$, then $AD + DB=AB$. Here, since $AD = x$, $DB = y$, and $AB = c$, we have $y + x=c$ by the Segment Addition Postulate.

Answer:

Segment Addition Postulate