Geometry proof practice worksheet with four problems involving triangles and angles.

Final Answer:
Proof 1:
1. PN ∥ ME (Given)
2. ∠P ≅ ∠M (Alternate Interior Angles Theorem)
3. ∠N ≅ ∠E (Alternate Interior Angles Theorem)
4. PN = ME (Given)
5. △PNO ≅ △MEO (ASA Congruence)

Proof 6:
1. RN ⊥ LG (Given)
2. ∠RNL and ∠GNL are right angles (Definition of perpendicular)
3. ∠RNL ≅ ∠GNL (All right angles are congruent)
4. K is midpoint of RN (Given)
5. RK ≅ NK (Definition of midpoint)
6. ∠RKL ≅ ∠NKL (Vertical angles are congruent)
7. △RKL ≅ △NKL (SAS Congruence)
8. ∠GKM ≅ ∠GKN (Corresponding parts of congruent triangles)

Proof 3:
1. XY bisects ∠WYZ (Given)
2. ∠WYX ≅ ∠ZYX (Definition of angle bisector)
3. ∠WXY ≅ ∠ZXY (Given)
4. YX = YX (Reflexive Property)
5. △WXY ≅ △ZXY (AAS Congruence)

Proof 4:
1. ∠ABC and ∠EDC are right angles (Given)
2. ∠ACB ≅ ∠ECD (Vertical angles are congruent)
3. AC = EC (Given)
4. △ABC ≅ △EDC (AAS Congruence)