Question

Fill in the correct reason for A, B, C, D, E, and F to complete the proof above.

Answer 1

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         ${}$                    Reason

$\overline{FG}$║$\overline{EH}$       ${}$                         Given

∠FGE ≅ ∠HEG       ${}$               Alternate interior angles theorem

$\overline{EG}$ ≅ $\overline{EG}$        ${}$                      Reflexive property

$\overline{FG}$ ≅ $\overline{EH}$       ${}$                       Given

ΔFEG ≅ ΔHEG       ${}$               SAS rule of congruency

$\overline{FE}$ ≅ $\overline{HG}$       ${}$                      CPCTC

EFGH is a parallelogram  ${}$    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