Question

x,y are the mid points of opposite side ab and dc of a paralleogram abcd . ay and dx are joined intersecting in p: cx and by are joined intersecting in q show that 1) axcy is a parallelogram 2) dxby is a parallelogram 3)pqcy is a parallelogram​

Answer 1

Step-by-step explanation:

ab=cd

so dy=ax=bx=cy

and ad=bc

so tri' dyx and xad are congruent (SAS)

as dy=ax

xy=ad

and angle dyx=L xad

Similarly tri' byc and ybx are congruent. In fact all 4 tri' are congruent. So figures formed by joining pairs of congruent tri' become parlgrms.

So

axcy and dxby are parlgrms.

Again pq divides parlgrm

pxqy in two congruent tri'.

So pq is parl to

both cd and ab.

And pqcy also becomes a parlgrm.