Question

$$overline{tw} cong overline{uv}$$ and $$overline{tu} cong overline{vw}$$. complete the proof that $$angle w cong angle u$$.

statement	reason
2 $$overline{tu} cong overline{vw}$$
3 $$overline{tv} cong overline{tv}$$
4 $$\triangle tuv cong \triangle wvt$$
5 $$angle w cong angle u$$

Explanation:

Step1: Identify Given Information

We are given that \(\overline{TW} \cong \overline{UV}\) and \(\overline{TU} \cong \overline{VW}\), and we need to prove \(\angle W \cong \angle U\).

Step2: Analyze Statement 1

Statement 1: \(\overline{TW} \cong \overline{UV}\)
Reason: Given (as it's provided in the problem statement that \(\overline{TW} \cong \overline{UV}\))

Step3: Analyze Statement 2

Statement 2: \(\overline{TU} \cong \overline{VW}\)
Reason: Given (as it's provided in the problem statement that \(\overline{TU} \cong \overline{VW}\))

Step4: Analyze Statement 3

Statement 3: \(\overline{TV} \cong \overline{TV}\)
Reason: Reflexive Property of Congruence (a segment is congruent to itself)

Step5: Analyze Statement 4

Statement 4: \(\triangle TUV \cong \triangle VWT\)
Reason: SSS (Side - Side - Side) Congruence Criterion (since \(\overline{TW} \cong \overline{UV}\), \(\overline{TU} \cong \overline{VW}\), and \(\overline{TV} \cong \overline{TV}\))

Step6: Analyze Statement 5

Statement 5: \(\angle W \cong \angle U\)
Reason: Corresponding Parts of Congruent Triangles are Congruent (CPCTC) (since \(\triangle TUV \cong \triangle VWT\), their corresponding angles \(\angle W\) and \(\angle U\) are congruent)

Answer:

For Statement 1, Reason: Given;
For Statement 2, Reason: Given;
For Statement 3, Reason: Reflexive Property of Congruence;
For Statement 4, Reason: SSS Congruence Criterion;
For Statement 5, Reason: CPCTC