Question

statement reason 1 △ruv ≅ △stv given 2 ru ≅ st cpctc 3 rv ≅ sv cpctc 4 tv ≅ uv cpctc 5 ∠ruv ≅ ∠stv cpctc 6 rt = rv + tv additive property of length 7 su = sv + uv additive property of length 8 rt = sv + uv substitution 9 rt = su transitive property of equality 10 △rst ≅ △sru |

Explanation:

Step1: Identify known congruences

We have $\triangle RUV \cong \triangle STV$ (Given), $\overline{RU} \cong \overline{ST}$ (CPCTC), $\overline{RT} \cong \overline{SU}$ (Proven in step 9), and $\overline{RS}$ is a common side to both $\triangle RST$ and $\triangle SRU$.

Step2: Apply SSS congruence rule

For $\triangle RST$ and $\triangle SRU$:

• $\overline{RS} \cong \overline{SR}$ (Reflexive Property of Congruence)
• $\overline{ST} \cong \overline{RU}$ (From step 2)
• $\overline{RT} \cong \overline{SU}$ (From step 9)

This satisfies the Side-Side-Side (SSS) Triangle Congruence Postulate.

Answer:

Side-Side-Side (SSS) Triangle Congruence Postulate