how to prove a Quadrilateral is a parallelogram

Question

Quadrilateral FAST has diagonals that intersect at point R. Which statement would not be sufficient to prove quadrilateral FAST is a parallelogram?  

a) FR ≅ SR and AR ≅ TR

b) FA ≅ ST and AS ≅ TF

c) AS ≅ TF and FA// TS

d) AS // FT and FA // TS

Explain why c is the answer. 

Answer 1

C is not sufficient because it could be an isosceles trapezoid (FA is parallel to TS and AS is congruent to TF, but AS and TF are not parallel / \)

If you want to use "two sides are congruent and parallel" to prove a quadrilateral is a parallelogram, it needs to be the same two sides that are both congruent and parallel.

A) sufficient because diagonals are bisected

B) sufficient because opposite sides are congruent

D) sufficient because opposite sides are parallel