Answer:
Step-by-step explanation:
Given: ABCD is a trapezoid.
Proof: Using the property of trapezoid that the bases of the trapezoid are parallel to each other.
From △AOD and △BOC, we have:
∠DAO=∠BCO (Alternate angles)
∠AOD=∠BOC( Vertically opposite angles)
Therefore, by AA similarity,
△AOD ∼ △BOC
Also, from ΔAOB and ΔCOD, we have
∠BAO=∠DCO (Alternate angles)
∠AOB=∠DOC(Vertically opposite angles)
Therefore, by AA similarity,
△AOB ∼ △COD
Hence proved.
