Answer to Question #95538 in Geometry for mashud

Question

ABCD is a quadrilateral and P and Q are midpoints of AC and BD respectively. Show that AB +AD+CB+CD= 4PQ

Answer 1

for trapezium. AB and CD trapezoid bases:

from the trapezoid property:

$PQ=(CD-AB)/2\\ 2PQ=CD-AB\Rightarrow 2PQ<CD+AB$

and

$2PQ<AD+CB\Rightarrow 4PQ<AB+AD+CB+CD$ . The statement of the question is not correct.