Geometry proof exercises with diagrams and blank tables for logical reasoning.

PROOF #3
1) ∠C ≅ ∠D, ∠E ≅ ∠F, CE ≅ DF 1) Given
2) △CEF ≅ △DFE 2) AAS Congruence Postulate
3) CF ≅ DE 3) CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
4) ∠CFE ≅ ∠DEF 4) CPCTC
5) ∠CFE and ∠DEF are alternate interior angles 5) Definition of alternate interior angles
6) CF || DE 6) If alternate interior angles are congruent, then the lines are parallel

PROOF #4
1) BD bisects ∠ABC 1) Given
2) BD bisects ∠ADC 2) Given
3) ∠ABD ≅ ∠CBD 3) Definition of angle bisector
4) ∠ADB ≅ ∠CDB 4) Definition of angle bisector
5) BD ≅ BD 5) Reflexive Property of Congruence
6) △ABD ≅ △CBD 6) ASA Congruence Postulate