Geometry worksheet featuring triangle congruence proofs with diagrams and given information.

1. Given: ∠W ≅ ∠Y, WX ≅ YZ, WZ ≅ XY
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- WX ≅ YZ (Given)
- WZ ≅ XY (Given)
- Therefore, ΔWXZ ≅ ΔYZX by SAS (Side-Angle-Side) Congruence.

2. Given: UW ≅ VW, UZ ≅ VZ
Prove: ΔUWZ ≅ ΔVWZ
Proof:
- UW ≅ VW (Given)
- UZ ≅ VZ (Given)
- WZ ≅ WZ (Reflexive Property)
- Therefore, ΔUWZ ≅ ΔVWZ by SSS (Side-Side-Side) Congruence.

3. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, WX ≅ YZ
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- WX ≅ YZ (Given)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.

4. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, WZ ≅ XY
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- WZ ≅ XY (Given)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.

5. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, XZ ≅ XZ
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- XZ ≅ XZ (Reflexive Property)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.

6. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, WZ ≅ XY
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- WZ ≅ XY (Given)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.

7. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, WX ≅ YZ
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- WX ≅ YZ (Given)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.

8. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, XZ ≅ XZ
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- XZ ≅ XZ (Reflexive Property)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.

9. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, WZ ≅ XY
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- WZ ≅ XY (Given)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.

10. Given: ∠W ≅ ∠Y, ∠X ≅ ∠Z, WX ≅ YZ
Prove: ΔWXZ ≅ ΔYZX
Proof:
- ∠W ≅ ∠Y (Given)
- ∠X ≅ ∠Z (Given)
- WX ≅ YZ (Given)
- Therefore, ΔWXZ ≅ ΔYZX by AAS (Angle-Angle-Side) Congruence.