Question

tw ≅ ux and ∠w ≅ ∠u. complete the proof that sx ≅ st.

statement
1 tw ≅ ux
2 ∠w ≅ ∠u
3 ∠s ≅ ∠s
4 △stw ≅ △sxu
5 sx ≅ st

reason

Explanation:

Step1: Given

The problem states that \(\overline{TW}\cong\overline{UX}\) and \(\angle W\cong\angle U\). So, the reason for statement 1 (\(\overline{TW}\cong\overline{UX}\)) and statement 2 (\(\angle W\cong\angle U\)) is "Given".

Step2: Reflexive Property of Congruence

For \(\angle S\cong\angle S\), by the reflexive property of congruence, any angle is congruent to itself.

Step3: AAS (Angle - Angle - Side) Congruence Criterion

In \(\triangle STW\) and \(\triangle SXU\), we have \(\angle W\cong\angle U\) (given), \(\angle S\cong\angle S\) (reflexive property), and \(\overline{TW}\cong\overline{UX}\) (given). So, by the AAS (Angle - Angle - Side) congruence criterion, \(\triangle STW\cong\triangle SXU\).

Step4: Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Since \(\triangle STW\cong\triangle SXU\), their corresponding parts are congruent. So, \(\overline{SX}\cong\overline{ST}\) (CPCTC).

Answer:

1. Given
2. Given
3. Reflexive Property of Congruence
4. AAS (Angle - Angle - Side)
5. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)