Question

△suv ≅ △tvu. complete the proof that ∠tsu ≅ ∠stv.

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

1. △suv ≅ △tvu (given)
2. (overline{sv} cong overline{tu}) (reason blank)
3. (overline{su} cong overline{tv}) (cpctc)
4. (overline{st} cong overline{st}) (reason blank)
5. △stv ≅ △tsu (sss)
6. ∠tsu ≅ ∠stv (reason blank))

Explanation:

Step1: Analyze Statement 2

Since \(\triangle SUV \cong \triangle TVU\), corresponding sides of congruent triangles are congruent (CPCTC). So \(\overline{SV} \cong \overline{TU}\) because they are corresponding sides of the given congruent triangles.

Step2: Analyze Statement 4

\(\overline{ST} \cong \overline{ST}\) is the reflexive property of congruence, which states that any segment is congruent to itself.

Step3: Analyze Statement 6

Since \(\triangle STV \cong \triangle TSU\) (from SSS in Step 5), corresponding angles of congruent triangles are congruent (CPCTC). So \(\angle TSU \cong \angle STV\) because they are corresponding angles of the congruent triangles \(\triangle STV\) and \(\triangle TSU\).

For Statement 2 Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
For Statement 4 Reason: Reflexive Property of Congruence
For Statement 6 Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

(Assuming we need to fill the reasons for each blank. Let's focus on each blank:

1. Statement 2: Reason is CPCTC (because \(\triangle SUV \cong \triangle TVU\), so corresponding sides \(\overline{SV}\) and \(\overline{TU}\) are congruent).
2. Statement 4: Reason is Reflexive Property (a segment is congruent to itself).
3. Statement 6: Reason is CPCTC (since \(\triangle STV \cong \triangle TSU\), corresponding angles \(\angle TSU\) and \(\angle STV\) are congruent).)

Answer:

• Statement 2 Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
• Statement 4 Reason: Reflexive Property of Congruence
• Statement 6 Reason: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

(If we need to fill each blank specifically:

• For the first blank (Statement 2 Reason): CPCTC
• For the second blank (Statement 4 Reason): Reflexive Property of Congruence
• For the third blank (Statement 6 Reason): CPCTC)