Question

show that the diagonal of a parallelogram divide it into four triangle of equal area​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

The ABCD is a parallelogram with AC and BD are diagonal

Diagonal of parallelogram bisect each other at point O

So O is the mid point of BD then BO=OD_____.(1)

And O is the mid point of AC then AO=OC____.(2)

In ΔABC

OA=OC From (2)

So BO is the median of ΔABC

Then area(ΔAOB)=area(ΔBOC)______&(3)

In ΔADC

OA=OC From (2)

So DO is the median of ΔABC

Then area(ΔAOD)=area(ΔCOD)______(4)

In ΔABD

OB=OD From (1)

So AO is the median of ΔABD

Then area(ΔAOB)=area(ΔAOD)_______.(5)

Then from (3) ,(4) and (5) we get

area(ΔAOB)=area(ΔBOC)=ΔCOD=ΔAOD

Then diagonal of parallelogram divide in four equal parts