Geometry worksheet featuring two triangle congruence proof exercises with diagrams and blank spaces for statements and reasons.

1. Given: ∠1 ≅ ∠2, AC bisects ∠DCB
Prove: △CDA ≅ △CBA

Statements Reasons
1. AC bisects ∠DCB 1. Given
2. ∠4 ≅ ∠3 2. Definition of angle bisector
3. ∠1 ≅ ∠2 3. Given
4. ∠1 + ∠3 ≅ ∠2 + ∠4 4. Addition Property of Equality (or Angle Addition Postulate)
5. ∠DCA ≅ ∠BCA 5. Substitution (from steps 2 and 4)
6. CA ≅ CA 6. Reflexive Property of Congruence
7. △CDA ≅ △CBA 7. ASA (Angle-Side-Angle) Congruence Postulate

2. Given: GE bisects ∠DEF, ∠D ≅ ∠F
Prove: △DGE ≅ △FGE

Statements Reasons
1. GE bisects ∠DEF 1. Given
2. ∠DEG ≅ ∠FEG 2. Definition of angle bisector
3. ∠D ≅ ∠F 3. Given
4. GE ≅ GE 4. Reflexive Property of Congruence
5. △DGE ≅ △FGE 5. AAS (Angle-Angle-Side) Congruence Theorem