Question

pls answer to get 30 points​

Answer 1

Step-by-step explanation:

Diagonals bisects each other.

So, PO = OR and SO = OQ.    ----- (1)

In ΔPQS, PO is median.

Since, median divided the triangle into two parts of equal area. we have,

area(PSO) = area(PQO)    ----- (2)

Similarly,

In ΔPQR, PO is median.

Therefore,

area(PQO) = area(QRO)   ----- (3)

Likewise,

In ΔQRS, RO is median.

Therefore,

area(QRO) = area(RSO)      ------- (4)

From (2),(3),(4) equations, we will get

Area(PSO) = Area(PQO) = Area(QRO) = Area(RSO)

Therefore, the diagonals divide it into four equal triangles of equal area.

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Answer 2

Step-by-step explanation:

we know that diagonal of a parallelogram bisect each other therefore A is equal to OC andDO is equal to OB in parallelogram ABCD

AC is the diagonal and O is the median of triangle divide it into two equal parts of equal triangles

this implies in triangle ABC, oc is median therefore ar(AOC)is equal to ar (BOC) (1)

similarly in triangle CBD, OB is median ar(COB) is equal to ar(BOD) (2)

in triangle BAD, OD is median ar(BOD) is equal to ar(AOD) (3)

NOW from 1,2 and 3 we get ar(AOC)=ar(BOC)=ar(BOD)=ar(AOD)

hence, proved