In A ABC , P and Q are respectively the mid-points of `AB` and `BC` and R is the mid-point of `A Pdot` Prove that: `ar ( PRQ)=1/2ar ( A R C)`

Explanation

We know that each median of a triangle divides it into two triangles of equal area.

Since, OR is a median of `triangleCAP`

`therefore` ar(`triangleCRA`)=1/2ar(`triangleCAP`)___1

Also, CP is a median of `triangleCAB`

ar(`triangleCAP`)=ar(`triangleCPB`)_______2

From 1 and 2

`therefore` ar(`triangleARC)=1/2(`triangleCPB)

PQ is the median of `trianglePBC`

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