Answer:
Explanation:
To prove UX ≅ SV based on the given information, we need to complete the missing statement in the proof. Let's analyze the given information and options to find the correct missing statement.
Given:
- Triangle STU is an equilateral triangle.
- ∠TXU ≅ ∠TVS.
We are trying to prove UX ≅ SV.
Let's consider the options provided:
Option A: △SXU ≅ △TVS
Option B: △UVX ≅ △SXV
Option C: △SWX ≅ △UWV
Option D: △TUX ≅ △TSV
To determine the missing statement, we need to find congruent triangles that involve UX and SV. Looking at the given triangle and the angles given, we observe that ∠TXU and ∠TVS are corresponding angles.
Corresponding angles suggest that triangles TUX and TVS have a congruent angle pair. Thus, we can determine that the missing statement is:
**Option D: △TUX ≅ △TSV**
Let's review the proof now:
Statement | Reason
1. ∠TXU ≅ ∠TVS | Given
2. ∠STV ≅ ∠UTX | Reflexive property
3. △STU is an equilateral triangle | Given
4. ST ≅ UT | Sides of an equilateral triangle are congruent
5. △TUX ≅ △TSV | AAS (Angle-Angle-Side)
6. UX ≅ SV | CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
Therefore, the missing statement in the proof is: **△TUX ≅ △TSV**.