Question

proof:

statements	reasons
2. $\angle cab \cong \angle dac$ <br> $\angle abc \cong \angle cbd$	reflexive property
3. $\triangle abc \sim \triangle acd$ <br> $\triangle abc \sim \triangle cbd$	aa similarity criteria
4. $\frac{ac}{ab} = \frac{ad}{ac}$ and $\frac{bc}{ab} = \frac{db}{bc}$	?
5. $ac^2 = (ab)(ad)$ <br> $bc^2 = (ab)(db)$	cross - multiplication
6. $ac^2 + bc^2 = (ab)(ad)+(ab)(db)$	addition
7. $ac^2 + bc^2 = ab(ad + db)$	distributive property
8. $ab = ad + db$	segment addition
9. $ac^2 + bc^2 = (ab)(ab)$	substitution
10. $ac^2 + bc^2 = ab^2$	multiplication

which reason completes the proof?
a. corresponding parts of similar triangles are congruent.
b. corresponding parts of congruent triangles are congruent.
c. corresponding sides of similar triangles are proportional.
d. corresponding sides of congruent triangles are proportional.

Explanation:

Step 3 established that pairs of triangles are similar. The proportions in step 4 are ratios of corresponding sides of these similar triangles, which follows the core property of similar triangles regarding their side lengths.

Answer:

C. Corresponding sides of similar triangles are proportional.