△UVY and △WXY are equilateral. Complete the proof that VW ≅ UX.
1. △UVY is equilateral
2. △WXY is equilateral
3. UY ≅ VY
4. WY ≅ XY
5. ∠UYX ≅ ∠VYW
6. △UXY ≅ △WXY
7. VW ≅ UX
△UVY and △WXY are equilateral. Complete the proof that VW ≅ UX.
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To prove that VW ≅ UX, we can use the properties of equilateral triangles and congruence.
1. Since △UVY is equilateral, all its sides are equal: UY ≅ VY ≅ UV.
2. Similarly, in △WXY, all sides are equal: WY ≅ XY ≅ WX.
3. From the information given: UY ≅ VY (step 3) and WY ≅ XY (step 4).
4. Angles ∠UYX and ∠VYW are equal as stated in step 5.
5. By the Angle-Side-Angle (ASA) postulate, we have sufficient information to establish that △UXY ≅ △WXY (step 6).
6. Since these triangles are congruent, their corresponding parts are equal. Thus, we can conclude that VW ≅ UX (step 7).
This establishes the proof that VW is congruent to UX. If you have more detailed questions or need further clarification, feel free to ask!