Geometry worksheet featuring triangle congruence proofs with diagrams and logical statements.

1. Given: UW ≅ VW, UX ≅ VX
Prove: ∠UWV ≅ ∠XWV
Proof:
1. UW ≅ VW (Given)
2. UX ≅ VX (Given)
3. WX ≅ WX (Reflexive Property)
4. △UWX ≅ △VWX (SSS Congruence)
5. ∠UWV ≅ ∠XWV (CPCTC)

2. Given: UV ≅ VW, WU ≅ WV
Prove: ∠U ≅ ∠V
Proof:
1. UV ≅ VW (Given)
2. WU ≅ WV (Given)
3. UW ≅ UW (Reflexive Property)
4. △UVW ≅ △VWU (SSS Congruence)
5. ∠U ≅ ∠V (CPCTC)

3. Given: UV ≅ VW, UZ ≅ VZ
Prove: ∠UWV ≅ ∠XWV
Proof:
1. UV ≅ VW (Given)
2. UZ ≅ VZ (Given)
3. WZ ≅ WZ (Reflexive Property)
4. △UWZ ≅ △VWZ (SSS Congruence)
5. ∠UWV ≅ ∠XWV (CPCTC)

4. Given: UW ≅ VW, UX ≅ VX
Prove: ∠UWX ≅ ∠VWX
Proof:
1. UW ≅ VW (Given)
2. UX ≅ VX (Given)
3. WX ≅ WX (Reflexive Property)
4. △UWX ≅ △VWX (SSS Congruence)
5. ∠UWX ≅ ∠VWX (CPCTC)

5. Given: UW ≅ VW, UX ≅ VX
Prove: ∠UWV ≅ ∠XWV
Proof:
1. UW ≅ VW (Given)
2. UX ≅ VX (Given)
3. WX ≅ WX (Reflexive Property)
4. △UWX ≅ △VWX (SSS Congruence)
5. ∠UWV ≅ ∠XWV (CPCTC)

6. Given: ∠U ≅ ∠V, ∠W ≅ ∠X
Prove: △UWV ≅ △VXW
Proof:
1. ∠U ≅ ∠V (Given)
2. ∠W ≅ ∠X (Given)
3. UV ≅ VW (Given)
4. △UWV ≅ △VXW (AAS Congruence)

7. Given: UW ≅ VW, UX ≅ VX
Prove: ∠UWV ≅ ∠XWV
Proof:
1. UW ≅ VW (Given)
2. UX ≅ VX (Given)
3. WX ≅ WX (Reflexive Property)
4. △UWX ≅ △VWX (SSS Congruence)
5. ∠UWV ≅ ∠XWV (CPCTC)

8. Given: ∠U ≅ ∠V, ∠W ≅ ∠X
Prove: △UWV ≅ △VXW
Proof:
1. ∠U ≅ ∠V (Given)
2. ∠W ≅ ∠X (Given)
3. UV ≅ VW (Given)
4. △UWV ≅ △VXW (AAS Congruence)