Question

$\triangle rst \cong \triangle rqu$. complete the proof that $\triangle qtu \cong \triangle sut$.

(image of a geometric figure with points u, q, r, s, t and a table with statements and reasons:

1. $\triangle rst \cong \triangle rqu$ - given
2. $\overline{qu} \cong \overline{st}$ - cpctc
3. $\overline{qr} \cong \overline{rs}$ - cpctc
4. $\overline{ru} \cong \overline{rt}$ - cpctc
5. $qt = qr + rt$ - blank for reason
6. $su = rs + ru$ - additive property of length
7. $qt = rs + ru$ - substitution
8. $qt = su$ - transitive property of equality
9. $\overline{tu} \cong \overline{tu}$ - reflexive property of congruence
10. $\triangle qtu \cong \triangle sut$ - sss)

Explanation:

Step1: Identify length addition rule

Segment $QT$ is composed of $QR$ and $RT$, so we use the additive property of length, which states that the total length of a segment is the sum of the lengths of its non-overlapping parts.

Step2: Match to the statement

The statement $QT = QR + RT$ directly follows this property, so the reason is the Additive Property of Length.

Answer:

Additive Property of Length