P and Q are respectively the mid points of side AB and BC of a triangle ABC and R is the mid point of AP show that,

{1} ar(PQR)= 1/2 ar(ARC)

{2} ar (RQC)=3/8 ar(ABC)

3) ar (pBQ) = ar(ARC)

** Given that**: P and Q are the mid points of side AB and BC of a triangle ABC and R is the mid-point of AP

__To prove: __

** Construction:** join PQ , RQ and RC

__Proof:__

**(3)**

CR is a median of

Also, CP is a median of

From (1) and (2), we get,

PQ is a median of,

From (3) and (4), we get,

Hence,

**(1)**

Since QP and QR medians of triangles QAB and QAP

And

From (6) and (7), we get,

From (5) and (8), we get,

Hence,

**(2)** Since CR is a median of,

…… (1)

Since RQ is median of,

Hence,

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