Trapezium properties

In the trapezium ABCD, AB || CD and diagonals are AC,BD:
Then
1. If the midpoints of diagonals are E,F then EF || AB || CD.
2. If the midpoints of BC,AD are P,Q then PQ || AB || CD and PQ = (AB+CD)/2.
3. If the diagonals AC,BD intersect at O then: 
3a. Triangles OAB and OCD are similar.
3b. Triangles OAD and OCB have same area.

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