Question

Show that diagonals of a parallelogram divide it into four equal area

Answer 1

In triangle ABD ,OA is median

ar(AOB)=ar(AOD)___(1)

In triangle ABC ,BO is median

ar(AOB)=ar(BOC)____(2)

In triangle BCD , CO is median

ar(BOC)=ar(COD)____(3)

from (1),(2),(3),we get

ar(AOB)=ar(BOC)=ar(COD)=ar(AOD)

Answer 2

Answer:

Step-by-step explanation:

In triangle QRS ,OR is median

ar(QOR)=ar(ROS)___(1)

In triangle RSP ,SO is median

ar(ROP)=ar(ROS)____(2)

In triangle PQS , PO is median

ar(POQ)=ar(POS)____(3)

from (1),(2),(3),we get

ar(ROS)=ar(POS)=ar(POQ)=ar(ROQ)