Question

Which condition is sufficient to show that quadrilateral DEFG is a parallelogram?

A. ∠GDE is supplementary to ∠DEF

B. ∠GDE is supplementary to ∠EFG

C. ∠GDE is supplementary to ∠DEF and ∠EFG

D. ∠GDE is supplementary to ∠DEF and ∠FGD

Answer 1

D. ∠GDE is supplementary to ∠DEF and ∠FGD

Explanation:

Did it on savvas

Answer 2

Option D

∠GDE is supplementary to ∠DEF and also supplementary to ∠FGD

Explanation:

To use the supplementary property to identify a parallelogram. The condition must be that that the same-side interior angles (consecutive angles) are supplementary.

Thus for parallelogram DEFG

D --------------------E

/ /

G---------------------F

Thus, we have it that the condition that is most sufficient to show that quadrilateral DEFG is a parallelogram is

∠GDE is supplementary to both ∠DEF and ∠FGD