Question

△tuv≅△svu. complete the proof that ∠sut≅∠svt.
1 △tuv≅△svu given
2 overline{sv}≅overline{tu} cpctc
3 overline{su}≅overline{tv} cpctc
4 overline{st}≅overline{st}
5 △stv≅△tsu
6 ∠sut≅∠svt

Explanation:

Step1: Reason for $\overline{ST}\cong\overline{ST}$

Reflexive property of congruence (a segment is congruent to itself).

Step2: Reason for $\triangle STV\cong\triangle TSU$

SSS (Side - Side - Side) congruence criterion. Since $\overline{SV}\cong\overline{TU}$, $\overline{SU}\cong\overline{TV}$, and $\overline{ST}\cong\overline{ST}$.

Step3: Reason for $\angle SUT\cong\angle SVT$

CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Answer:

1. Reflexive property of congruence; 5. SSS Congruence; 6. CPCTC.