Question

Fill in the blanks:

If △ ABC & △ DEF are two triangles such that AB, BC are respectively equal and parallel to DE, EF, then show that

Assertion (A): In △ABC, E and F are the midpoints of AC and AB respectively. The altitude AP at BC intersects FE at Q. Then, AQ = QP. Reason (R): Q is the midpoint of AP.

ABCD is a rhombus and P,Q,R,S are mid-points of AB, BC,CD and DA respectively. Prove that quadrilateral PQRS is a rectangle.