statement 1
GHIJ is a parallelogram ----------------> given
N 2
GH=JI -------------> by definition of a parallelogram (opposite sides are congruent)
N3
GP=IQ ------> given
N4
GH=GP+PH ----------> by addition segment postulate
GP=GH-PH
N5
JI=JQ+IQ ---------> by addition segment postulate
IQ=JI-JQ
N6
GH-PH=JI-JQ -------> by substitution
PH=JQ
N7
m by alternate interior angles
N8
m definition of right angle
N9
m definition of right angle
N10
triangle JXQ is congruent to triangle HXP ------> by ASA
N 11
PX≅QX -------> by corresponding sides in congruent triangles