1. XJ ≅ YK; XP ≅ YP ∠ZXJ ≅ ∠ZYK
1. given
2. ∠JZX and ∠KZY are vertical angles
2.def. of vertical angles
3. ∠JZX ≅ ∠KZY
3. vertical angles are ≅
4. △JZX ≅ △KZY
4. AAS
5. ∠XJZ ≅ ∠YKZ
5. CPCTC
6. ∠XPY ≅ ∠XPY
6. reflexive property
7. △PYJ ≅ △PXK
7. AAS
8. JY ≅ KX
8. CPCTC