What is the name of the missing polygon in this pattern?

dodecagon, decagon, octagon, quadrilateral

a. pentagon

b. triangle

c. hexagon

d. heptagon

Pentagon in the missing shape in the family 

The statement that  heather can use to prove that segment dt is equal to segment tb is  ta ≅ tc or segment ta is congruent to segment tc. also, he  used the alternate interior angles theorem to show that angle abd is congruent to angle cdb and that angle bac is congruent to dca.  this is because  you are given a  quadrilateral abcd, the diagonals intersect at point t. the distances at the corners of each angle to the center at point t is always equal to the other corners as well and that is why this is the answer. they have the same distance because they are intersected at a common point.