Question

in the diagram below, $\triangle svu \cong \triangle tuv$.
complete the proof that $\angle stv \cong \angle tsu$.

	statement	reason
1	$\triangle svu \cong \triangle tuv$	given
2	$\overline{sv} \cong \overline{tu}$
3	$\overline{su} \cong \overline{tv}$	corresponding parts of congruent triangles are congruent.
4	$\overline{st} \cong \overline{st}$	reflexive property of congruence
5	$\triangle stv \cong \triangle tsu$
6	$\angle stv \cong \angle tsu$

Explanation:

Step1: Determine Reason for \( \overline{SV} \cong \overline{TU} \)

Since \( \triangle SVU \cong \triangle TUV \), corresponding sides of congruent triangles are congruent (CPCTC). So the reason for \( \overline{SV} \cong \overline{TU} \) is "Corresponding parts of congruent triangles are congruent."

Step2: Determine Reason for \( \triangle STV \cong \triangle TSU \)

We have \( \overline{SV} \cong \overline{TU} \), \( \overline{SU} \cong \overline{TV} \), and \( \overline{ST} \cong \overline{ST} \). By the Side - Side - Side (SSS) Congruence Postulate, if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. So \( \triangle STV \cong \triangle TSU \) by SSS.

Step3: Determine Reason for \( \angle STV \cong \angle TSU \)

Since \( \triangle STV \cong \triangle TSU \), corresponding angles of congruent triangles are congruent (CPCTC). So the reason is "Corresponding parts of congruent triangles are congruent."

Answer:

• For statement 2: Corresponding parts of congruent triangles are congruent.
• For statement 5: Side - Side - Side (SSS) Congruence Postulate.
• For statement 6: Corresponding parts of congruent triangles are congruent.