Answer:
(A) Alternate interior angles theorem
(B) Reflexive property
(C) Given
(D) SAS rule of congruency
(E) CPCTC
(F) If both pairs of opposite sides of a parallelogram are congruent, then the quadrilateral is a parallelogram
Step-by-step explanation:
The two column proof required to prove that EFGH is a parallelogram is presented as follows;
Statement [tex]{}[/tex] Reason
[tex]\overline{FG}[/tex]║[tex]\overline{EH}[/tex] [tex]{}[/tex] Given
∠FGE ≅ ∠HEG [tex]{}[/tex] Alternate interior angles theorem
[tex]\overline{EG}[/tex] ≅ [tex]\overline{EG}[/tex] [tex]{}[/tex] Reflexive property
[tex]\overline{FG}[/tex] ≅ [tex]\overline{EH}[/tex] [tex]{}[/tex] Given
ΔFEG ≅ ΔHEG [tex]{}[/tex] SAS rule of congruency
[tex]\overline{FE}[/tex] ≅ [tex]\overline{HG}[/tex] [tex]{}[/tex] CPCTC
EFGH is a parallelogram [tex]{}[/tex] If both pairs of opposite sides of a parallelogram are congruent, then the quadrilateral is a parallelogram
Where CPCTC stands for Congruent Parts of Congruent Triangles are Congruent
