90 POINTS- Please help with this geometry question! I have the answer because I assumed it was congruent, but I don't have the statement reasons.

A Δ DOC = 6 in²

Step-by-step explanation:

Look at the attached graph

∵ ABCD is a trapezoid with legs AB and CD

∴ AD // BC

In Δs ABC and DCB

∵ BC is a common base

→ The heights of the Δs drawn from the points A and D to the base

   BC are equal because the line joining A and D, AD is parallel to

   the base BC

∴ Their heights are equal

→ Triangles of the same base and equal heights are equal in areas

∴ A Δ ABC = A Δ DCB

∵ A Δ ABC = A Δ ABO + A Δ BOC

∵ A Δ DCB = A Δ DOC + A Δ COB

→ Equate their right sides

∴ A Δ ABO + A Δ BOC = A Δ DOC + A Δ COB

∵ A Δ BOC = A Δ COB ⇒ common triangle

∴ A Δ ABO = A Δ DOC

∵ A Δ ABO = 6 in²

∴ A Δ DOC = 6 in²